https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Bluecarneal&feedformat=atomAoPS Wiki - User contributions [en]2021-06-21T22:53:57ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=Getting_Started_With_Python_Programming&diff=105486Getting Started With Python Programming2019-04-25T01:24:22Z<p>Bluecarneal: /* Using the Python Shell */</p>
<hr />
<div>This guide takes you through the process of getting started with programming using the Python programming language. The only language that AoPS teaches (as of March 2018) in a class is Python. <br />
<br />
The sections flow from one to the next so it's recommended to read through this document in order from top to bottom. <br />
<br />
If you find that this is too easy, '''make sure you've read everything through (at least roughly)''', and check out [[Basic Programming With Python]].<br />
<br />
==Installing Python==<br />
<br />
Python is a useful and popular computer programming language. Confusingly, Python has two major versions (2 and 3) and they are not fully compatible. We recommend using the most recent release of version 3. (This is the version that our [http://www.artofproblemsolving.com/School/courseinfo.php?course_id=python1 Introduction to Programming with Python course] uses -- if you are enrolled in that class, you '''must''' have Python 3.) There is absolutely nothing wrong with Python 2, as it is what most of today's technology supports and uses, but Python 3 is well on the way of replacing Python 2, so it will be more useful in a few years.<br />
<br />
Python is open-source software and it is '''free''' to install and use. Here are installation instructions:<br />
<br />
#Go to the Python download page at http://www.python.org/downloads. Near the top of the page, there will be a list of download links for the Python 3.7.x installer. (The x will be replaced by a number -- as of April 2019 the version is 3.7.3.) If you are given multiple options, click on the link that corresponds to your computer type (Windows or Mac, 32-bit or 64-bit -- if you're not sure, use the 32-bit version.) Some browsers will save the file automatically, others may pop up a box asking you if you want to save the file, in which case you should click the "save file" option. Depending on how your browser is configured, you may be asked where to save the file. If this is the case, keep track of where you save the installer.<br />
#Find where the installer was downloaded and double click on it to run it. On most browsers, you should simply be able to double-click the installer from the browser's "Downloads" window or menu. You may also have to click "Run" or "Yes" to a security window -- do this if necessary.<br />
#The setup wizard should launch. You should just click "Next" for every option in the setup wizard (i.e. use the defaults), unless you have some specific reason not to.<br />
#Familiarize yourself with the Python shell and IDLE text editor by running through the two sections below.<br />
<br />
==Programming==<br />
<br />
Yay, it's time to program! The next few sections will talk about some very basic programming. We will program a few programs as a demonstration.<br />
<br />
===Using the Python Shell===<br />
The program that you'll use to run Python is called IDLE. It may be listed on your computer as "IDLE (Python GUI)". <br />
* On a Mac, IDLE should be in the Applications folder. <br />
* On Windows, IDLE should be accessible from the Start menu in a folder named "Python 3.7" (or something similar).<br />
The icon for IDLE looks something like this [[File:Idleicon.png]] or this [[File:Idleiconmac.png]].<br />
<br />
When you first open IDLE, you'll see the Python Shell (the numbers on your shell might be different than those shown below): <br />
<br />
[[File:Idle2-1.png]]<br />
<br />
(The screenshots in this article are taken using IDLE on a Mac with the font increased. Thus IDLE may look a little bit different for you but should still function similarly.)<br />
<br />
Note that the first line is the version of Python, which is 3.1.2 in the screenshot but should be 3.7.something if you installed it as directed above. Another thing to note is that in the lower right hand corner of the Python Shell you can see that it says "Ln: 4 Col: 4". This is just telling you where in the document your cursor is. In this case it's on line 4 and over in column 4. (The line and column number may be slightly different for your installation.)<br />
<br />
When you first start up Python on a Mac, you might get the following warning:<br />
: >>> WARNING: The version of Tcl/Tk (8.5.9) in use may be unstable.<br />
: Visit http://www.python.org/download/mac/tcltk/ for current information.<br />
If you get this warning, you'll need to update a graphics driver on your computer. Follow the link shown above and download and install the ActiveTcl driver that's recommended for the version of OS X that your Mac is running. This most likely will be 8.5.15.0, which you can also download directly from http://www.activestate.com/activetcl/downloads (IMPORTANT: you only need to do this step if you get the warning printed above when you start IDLE for the first time. If you don't get the warning, then everything is good to go.)<br />
<br />
<br />
The Python Shell is very useful for quick one-liners and short sequences of commands:<br />
<br />
[[File:Idle2-2.2.png]]<br />
<br />
Here we see a number of familiar operations: + for addition, - for subtraction, * for multiplication, and / for division. The last operation shown in the example, denoted by **, happens to be exponentiation. One neat feature to note about Python is that it can store arbitrarily large numbers (limited by the amount of memory your computer has). Trying some hefty exponentiation, we can see that we can compute with some pretty big numbers such as <math>2^{1000}</math> as illustrated below.<br />
<br />
[[File:Idle2-3.png]]<br />
<br />
While Python can make for a pretty good calculator, it can do a whole lot more. One example is when dealing with strings as follows:<br />
<br />
[[File:Idle2-4.png]]<br />
<br />
Here we are concatenating the three strings "python", "is", and "cool" by using the + operator. Notice that previously we used + to add numbers but now with strings, Python concatenates them! You may also note that the output of the operation gives us a string with single quotes around it. In Python, you are able to use single quotes or double quotes to denote a string. You can use them interchangeably.<br />
<br />
As a final example, we can even write code in the Python Shell that extends beyond a single line as shown below. We also see our first example of a <math>\verb=for=</math> loop.<br />
<br />
[[File:Idle2-5.png]]<br />
<br />
As you type the above, the Python Shell will automatically indent the second line for you. To let the Python Shell know that you're done and are ready for it to run your code, you'll need to put in an extra blank line by hitting the Enter key again. At that point it should run your code and print your output.<br />
<br />
Take some time to play around with the Python Shell. You'll want to go through a more extensive introduction to programming to learn the full extent of what you can do with Python, but you can still do some pretty nifty stuff by just playing around. The Python Shell also has an extensive built-in help system -- just type '''help()''' at the ">>>" prompt to get started and then follow the instructions it gives you.<br />
<br />
===The IDLE Text Editor===<br />
For most programming needs, you'll want to edit your program in a separate document and then run it. Luckily, IDLE comes with its own built-in text editor.<br />
<br />
To get started, go to the File menu of the Python Shell and click on "New Window". This should give you a blank document with the title "Untitled" as shown below:<br />
<br />
[[File:Idle2-6.png]]<br />
<br />
You'll need to save your file before running it, so you might as well save it now. Make sure that you name your file with a file name with a file extension of .py (so it ends with .py), so your computer knows that it is a Python program. Here, we save ours as test.py:<br />
<br />
[[File:Idle2-7.png]]<br />
<br />
To get acquainted with the text editor, let's write our first Python program! Let's write a program that will do the following task:<br />
<br />
'''Print all the integers from 1 to 50 inclusive.'''<br />
<br />
We can achieve this by using a loop that can loop through all the integers. Luckily, Python has a function just for doing that! We use a for loop with the following code:<br />
<br />
[[File:Test_.png]]<br />
<br />
Note that as you type, the keywords like "for", "in", "range" and "print" get colored in orange or purple!<br />
Also, note that you must copy the exact same indentation. Even though the editor automatically indents for you when you type <code>for i in range(1, 51):</code>, proper indentation in Python is super important! If you don't do it correctly, the program will not compile correctly.<br />
<br />
You can indent by pressing Tab on your keyboard.<br />
<br />
This for loop means to iterate from 1 to 51 excluding the 51 and including the 1. Every iteration, Python will print out the number that it is iterating through.<br />
<br />
Now that you've written this code, you probably want to run it and test it out. You can do so by going to the Run menu and hitting "Run Module" (or by pressing F5 on your keyboard). The ===RESTART=== line means that Python is clearing all the work you've previously done before it starts running your program. The program should execute and print all the integers to the Python Shell. If it didn't, then make sure your code exactly matches the code above.<br />
<br />
[[File:Test__results.png]]<br />
<br />
If your code worked, congratulations! You have written your very first program! Now, let's try another more useful one.<br />
<br />
'''Find the sum of all the positive multiples of 3 below 1000.'''<br />
<br />
We first need to create a new file. Go into the Python Shell and click on New Window again. Remember, we must save our file first. We can save it as test2.py. Now, on to the coding!<br />
We can solve this by keeping a running total: we'll start with the smallest positive multiple of 3 and go up one multiple at a time keeping track of the sum, stopping once we hit 1000. We can do this with the following code:<br />
<br />
[[File:Idle2-8.png]]<br />
<br />
This is called a while loop. While loops keep iterating until a statement becomes false.<br />
Notice that as you type the above code, the keywords ("while" and "print") will automatically get colored -- this makes the code easier to read. Also, after typing the line "while i < 1000:", the editor will automatically start indenting for you. When you get to the line "print(total)", you'll need to use the backspace key to remove the indentation. It is important that the code look exactly like it does in the screenshot above. Again, in Python, proper indentation is very important!<br />
<br />
This program basically works by incrementing the variable <math>\verb=i=</math> by 3 every time and adding it to the variable <math>\verb=total=</math>. The <math>\verb%+=%</math> operation might be intimidating at first. However, the statement <math>\verb%i += 3%</math> is just a shorthand for <math>\verb%i = i + 3%</math>. (So <math>\verb%a += b%</math> means <math>\verb&a = a + b&</math>.)<br />
<br />
Run your program, and you should get this:<br />
<br />
[[File:Idle2-9.png]]<br />
<br />
Again, the ===RESTART=== line just means that Python is clearing all the work you've previously done before it starts running your program. Then, the program runs and we get our answer, 166833. If you instead get an error message or a different answer, check that your program exactly matches the screenshot above, and try it again.<br />
<br />
Congrats! You have written your first two Python programs!<br />
<br />
==What's Next?==<br />
<br />
Now that you've learned the very basics of getting Python going, there's a bunch of tutorials you can look at which are [http://wiki.python.org/moin/BeginnersGuide/NonProgrammers listed] on the Python website. Go check them out! Another great resource is "Stack Overflow," a forums website built for people who would like to talk about, and get help with programming. It is also recommended that you check out a wiki article discussing more advanced python, namely [[Basic Programming With Python]].<br />
<br />
Or, you can take our Introduction to Programming with Python online course!</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Getting_Started_With_Python_Programming&diff=105485Getting Started With Python Programming2019-04-25T01:23:55Z<p>Bluecarneal: /* Installing Python */</p>
<hr />
<div>This guide takes you through the process of getting started with programming using the Python programming language. The only language that AoPS teaches (as of March 2018) in a class is Python. <br />
<br />
The sections flow from one to the next so it's recommended to read through this document in order from top to bottom. <br />
<br />
If you find that this is too easy, '''make sure you've read everything through (at least roughly)''', and check out [[Basic Programming With Python]].<br />
<br />
==Installing Python==<br />
<br />
Python is a useful and popular computer programming language. Confusingly, Python has two major versions (2 and 3) and they are not fully compatible. We recommend using the most recent release of version 3. (This is the version that our [http://www.artofproblemsolving.com/School/courseinfo.php?course_id=python1 Introduction to Programming with Python course] uses -- if you are enrolled in that class, you '''must''' have Python 3.) There is absolutely nothing wrong with Python 2, as it is what most of today's technology supports and uses, but Python 3 is well on the way of replacing Python 2, so it will be more useful in a few years.<br />
<br />
Python is open-source software and it is '''free''' to install and use. Here are installation instructions:<br />
<br />
#Go to the Python download page at http://www.python.org/downloads. Near the top of the page, there will be a list of download links for the Python 3.7.x installer. (The x will be replaced by a number -- as of April 2019 the version is 3.7.3.) If you are given multiple options, click on the link that corresponds to your computer type (Windows or Mac, 32-bit or 64-bit -- if you're not sure, use the 32-bit version.) Some browsers will save the file automatically, others may pop up a box asking you if you want to save the file, in which case you should click the "save file" option. Depending on how your browser is configured, you may be asked where to save the file. If this is the case, keep track of where you save the installer.<br />
#Find where the installer was downloaded and double click on it to run it. On most browsers, you should simply be able to double-click the installer from the browser's "Downloads" window or menu. You may also have to click "Run" or "Yes" to a security window -- do this if necessary.<br />
#The setup wizard should launch. You should just click "Next" for every option in the setup wizard (i.e. use the defaults), unless you have some specific reason not to.<br />
#Familiarize yourself with the Python shell and IDLE text editor by running through the two sections below.<br />
<br />
==Programming==<br />
<br />
Yay, it's time to program! The next few sections will talk about some very basic programming. We will program a few programs as a demonstration.<br />
<br />
===Using the Python Shell===<br />
The program that you'll use to run Python is called IDLE. It may be listed on your computer as "IDLE (Python GUI)". <br />
* On a Mac, IDLE should be in the Applications folder. <br />
* On Windows, IDLE should be accessible from the Start menu in a folder named "Python 3.6" (or something similar).<br />
The icon for IDLE looks something like this [[File:Idleicon.png]] or this [[File:Idleiconmac.png]].<br />
<br />
When you first open IDLE, you'll see the Python Shell (the numbers on your shell might be different than those shown below): <br />
<br />
[[File:Idle2-1.png]]<br />
<br />
(The screenshots in this article are taken using IDLE on a Mac with the font increased. Thus IDLE may look a little bit different for you but should still function similarly.)<br />
<br />
Note that the first line is the version of Python, which is 3.1.2 in the screenshot but should be 3.6.something if you installed it as directed above. Another thing to note is that in the lower right hand corner of the Python Shell you can see that it says "Ln: 4 Col: 4". This is just telling you where in the document your cursor is. In this case it's on line 4 and over in column 4. (The line and column number may be slightly different for your installation.)<br />
<br />
When you first start up Python on a Mac, you might get the following warning:<br />
: >>> WARNING: The version of Tcl/Tk (8.5.9) in use may be unstable.<br />
: Visit http://www.python.org/download/mac/tcltk/ for current information.<br />
If you get this warning, you'll need to update a graphics driver on your computer. Follow the link shown above and download and install the ActiveTcl driver that's recommended for the version of OS X that your Mac is running. This most likely will be 8.5.15.0, which you can also download directly from http://www.activestate.com/activetcl/downloads (IMPORTANT: you only need to do this step if you get the warning printed above when you start IDLE for the first time. If you don't get the warning, then everything is good to go.)<br />
<br />
<br />
The Python Shell is very useful for quick one-liners and short sequences of commands:<br />
<br />
[[File:Idle2-2.2.png]]<br />
<br />
Here we see a number of familiar operations: + for addition, - for subtraction, * for multiplication, and / for division. The last operation shown in the example, denoted by **, happens to be exponentiation. One neat feature to note about Python is that it can store arbitrarily large numbers (limited by the amount of memory your computer has). Trying some hefty exponentiation, we can see that we can compute with some pretty big numbers such as <math>2^{1000}</math> as illustrated below.<br />
<br />
[[File:Idle2-3.png]]<br />
<br />
While Python can make for a pretty good calculator, it can do a whole lot more. One example is when dealing with strings as follows:<br />
<br />
[[File:Idle2-4.png]]<br />
<br />
Here we are concatenating the three strings "python", "is", and "cool" by using the + operator. Notice that previously we used + to add numbers but now with strings, Python concatenates them! You may also note that the output of the operation gives us a string with single quotes around it. In Python, you are able to use single quotes or double quotes to denote a string. You can use them interchangeably.<br />
<br />
As a final example, we can even write code in the Python Shell that extends beyond a single line as shown below. We also see our first example of a <math>\verb=for=</math> loop.<br />
<br />
[[File:Idle2-5.png]]<br />
<br />
As you type the above, the Python Shell will automatically indent the second line for you. To let the Python Shell know that you're done and are ready for it to run your code, you'll need to put in an extra blank line by hitting the Enter key again. At that point it should run your code and print your output.<br />
<br />
Take some time to play around with the Python Shell. You'll want to go through a more extensive introduction to programming to learn the full extent of what you can do with Python, but you can still do some pretty nifty stuff by just playing around. The Python Shell also has an extensive built-in help system -- just type '''help()''' at the ">>>" prompt to get started and then follow the instructions it gives you.<br />
<br />
===The IDLE Text Editor===<br />
For most programming needs, you'll want to edit your program in a separate document and then run it. Luckily, IDLE comes with its own built-in text editor.<br />
<br />
To get started, go to the File menu of the Python Shell and click on "New Window". This should give you a blank document with the title "Untitled" as shown below:<br />
<br />
[[File:Idle2-6.png]]<br />
<br />
You'll need to save your file before running it, so you might as well save it now. Make sure that you name your file with a file name with a file extension of .py (so it ends with .py), so your computer knows that it is a Python program. Here, we save ours as test.py:<br />
<br />
[[File:Idle2-7.png]]<br />
<br />
To get acquainted with the text editor, let's write our first Python program! Let's write a program that will do the following task:<br />
<br />
'''Print all the integers from 1 to 50 inclusive.'''<br />
<br />
We can achieve this by using a loop that can loop through all the integers. Luckily, Python has a function just for doing that! We use a for loop with the following code:<br />
<br />
[[File:Test_.png]]<br />
<br />
Note that as you type, the keywords like "for", "in", "range" and "print" get colored in orange or purple!<br />
Also, note that you must copy the exact same indentation. Even though the editor automatically indents for you when you type <code>for i in range(1, 51):</code>, proper indentation in Python is super important! If you don't do it correctly, the program will not compile correctly.<br />
<br />
You can indent by pressing Tab on your keyboard.<br />
<br />
This for loop means to iterate from 1 to 51 excluding the 51 and including the 1. Every iteration, Python will print out the number that it is iterating through.<br />
<br />
Now that you've written this code, you probably want to run it and test it out. You can do so by going to the Run menu and hitting "Run Module" (or by pressing F5 on your keyboard). The ===RESTART=== line means that Python is clearing all the work you've previously done before it starts running your program. The program should execute and print all the integers to the Python Shell. If it didn't, then make sure your code exactly matches the code above.<br />
<br />
[[File:Test__results.png]]<br />
<br />
If your code worked, congratulations! You have written your very first program! Now, let's try another more useful one.<br />
<br />
'''Find the sum of all the positive multiples of 3 below 1000.'''<br />
<br />
We first need to create a new file. Go into the Python Shell and click on New Window again. Remember, we must save our file first. We can save it as test2.py. Now, on to the coding!<br />
We can solve this by keeping a running total: we'll start with the smallest positive multiple of 3 and go up one multiple at a time keeping track of the sum, stopping once we hit 1000. We can do this with the following code:<br />
<br />
[[File:Idle2-8.png]]<br />
<br />
This is called a while loop. While loops keep iterating until a statement becomes false.<br />
Notice that as you type the above code, the keywords ("while" and "print") will automatically get colored -- this makes the code easier to read. Also, after typing the line "while i < 1000:", the editor will automatically start indenting for you. When you get to the line "print(total)", you'll need to use the backspace key to remove the indentation. It is important that the code look exactly like it does in the screenshot above. Again, in Python, proper indentation is very important!<br />
<br />
This program basically works by incrementing the variable <math>\verb=i=</math> by 3 every time and adding it to the variable <math>\verb=total=</math>. The <math>\verb%+=%</math> operation might be intimidating at first. However, the statement <math>\verb%i += 3%</math> is just a shorthand for <math>\verb%i = i + 3%</math>. (So <math>\verb%a += b%</math> means <math>\verb&a = a + b&</math>.)<br />
<br />
Run your program, and you should get this:<br />
<br />
[[File:Idle2-9.png]]<br />
<br />
Again, the ===RESTART=== line just means that Python is clearing all the work you've previously done before it starts running your program. Then, the program runs and we get our answer, 166833. If you instead get an error message or a different answer, check that your program exactly matches the screenshot above, and try it again.<br />
<br />
Congrats! You have written your first two Python programs!<br />
<br />
==What's Next?==<br />
<br />
Now that you've learned the very basics of getting Python going, there's a bunch of tutorials you can look at which are [http://wiki.python.org/moin/BeginnersGuide/NonProgrammers listed] on the Python website. Go check them out! Another great resource is "Stack Overflow," a forums website built for people who would like to talk about, and get help with programming. It is also recommended that you check out a wiki article discussing more advanced python, namely [[Basic Programming With Python]].<br />
<br />
Or, you can take our Introduction to Programming with Python online course!</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2006_AMC_10B_Problems&diff=870952006 AMC 10B Problems2017-08-18T20:36:59Z<p>Bluecarneal: /* See also */</p>
<hr />
<div>== Problem 1 ==<br />
What is <math> (-1)^{1} + (-1)^{2} + ... + (-1)^{2006} </math> ?<br />
<br />
<math> \mathrm{(A) \ } -2006\qquad \mathrm{(B) \ } -1\qquad \mathrm{(C) \ } 0\qquad \mathrm{(D) \ } 1\qquad \mathrm{(E) \ } 2006 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
For real numbers <math>x</math> and <math>y</math>, define <math> x \mathop{\spadesuit} y = (x+y)(x-y) </math>. What is <math> 3 \mathop{\spadesuit} (4 \mathop{\spadesuit} 5) </math>?<br />
<br />
<math> \mathrm{(A) \ } -72\qquad \mathrm{(B) \ } -27\qquad \mathrm{(C) \ } -24\qquad \mathrm{(D) \ } 24\qquad \mathrm{(E) \ } 72 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
A football game was played between two teams, the Cougars and the Panthers. The two teams scored a total of 34 points, and the Cougars won by a margin of 14 points. How many points did the Panthers score? <br />
<br />
<math> \mathrm{(A) \ } 10\qquad \mathrm{(B) \ } 14\qquad \mathrm{(C) \ } 17\qquad \mathrm{(D) \ } 20\qquad \mathrm{(E) \ } 24 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 3|Solution]]<br />
<br />
== Problem 4 ==<br />
Circles of diameter 1 inch and 3 inches have the same center. The smaller circle is painted red, and the portion outside the smaller circle and inside the larger circle is painted blue. What is the ratio of the blue-painted area to the red-painted area? <br />
<br />
<math> \mathrm{(A) \ } 2\qquad \mathrm{(B) \ } 3\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 8\qquad \mathrm{(E) \ } 9 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 4|Solution]]<br />
<br />
== Problem 5 ==<br />
A <math> 2 \times 3 </math> rectangle and a <math> 3 \times 4 </math> rectangle are contained within a square without overlapping at any point, and the sides of the square are parallel to the sides of the two given rectangles. What is the smallest possible area of the square? <br />
<br />
<math> \mathrm{(A) \ } 16\qquad \mathrm{(B) \ } 25\qquad \mathrm{(C) \ } 36\qquad \mathrm{(D) \ } 49\qquad \mathrm{(E) \ } 64 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 5|Solution]]<br />
<br />
== Problem 6 ==<br />
A region is bounded by semicircular arcs constructed on the side of a square whose sides measure <math> \frac{2}{\pi} </math>, as shown. What is the perimeter of this region? <br />
<br />
<asy><br />
unitsize(1cm);<br />
defaultpen(.8);<br />
<br />
filldraw( circle( (0,1), 1 ), lightgray, black );<br />
filldraw( circle( (0,-1), 1 ), lightgray, black );<br />
filldraw( circle( (1,0), 1 ), lightgray, black );<br />
filldraw( circle( (-1,0), 1 ), lightgray, black );<br />
filldraw( (-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle, lightgray, black );<br />
</asy><br />
<br />
<math> \mathrm{(A) \ } \frac{4}{\pi}\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } \frac{8}{\pi}\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ } \frac{16}{\pi} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 6|Solution]]<br />
<br />
== Problem 7 ==<br />
Which of the following is equivalent to <math> \sqrt{\frac{x}{1-\frac{x-1}{x}}} </math> when <math> x < 0 </math>?<br />
<br />
<math> \mathrm{(A) \ } -x\qquad \mathrm{(B) \ } x\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } \sqrt{\frac{x}{2}}\qquad \mathrm{(E) \ } x\sqrt{-1} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 7|Solution]]<br />
<br />
== Problem 8 ==<br />
A square of area 40 is inscribed in a semicircle as shown. What is the area of the semicircle? <br />
<br />
<asy><br />
unitsize(1cm);<br />
defaultpen(.8);<br />
<br />
draw( (-sqrt(5),0) -- (sqrt(5),0), dashed );<br />
draw( (-1,0)--(-1,2)--(1,2)--(1,0)--cycle );<br />
draw( arc( (0,0), sqrt(5), 0, 180 ) );<br />
</asy><br />
<br />
<math> \mathrm{(A) \ } 20\pi\qquad \mathrm{(B) \ } 25\pi\qquad \mathrm{(C) \ } 30\pi\qquad \mathrm{(D) \ } 40\pi\qquad \mathrm{(E) \ } 50\pi </math><br />
<br />
[[2006 AMC 10B Problems/Problem 8|Solution]]<br />
<br />
== Problem 9 ==<br />
Francesca uses 100 grams of lemon juice, 100 grams of sugar, and 400 grams of water to make lemonade. There are 25 calories in 100 grams of lemon juice and 386 calories in 100 grams of sugar. Water contains no calories. How many calories are in 200 grams of her lemonade? <br />
<br />
<math> \mathrm{(A) \ } 129\qquad \mathrm{(B) \ } 137\qquad \mathrm{(C) \ } 174\qquad \mathrm{(D) \ } 233\qquad \mathrm{(E) \ } 411 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 9|Solution]]<br />
<br />
== Problem 10 ==<br />
In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle? <br />
<br />
<math> \mathrm{(A) \ } 43\qquad \mathrm{(B) \ } 44\qquad \mathrm{(C) \ } 45\qquad \mathrm{(D) \ } 46\qquad \mathrm{(E) \ } 47 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 10|Solution]]<br />
<br />
== Problem 11 ==<br />
What is the tens digit in the sum <math> 7!+8!+9!+...+2006!</math><br />
<br />
<math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 3\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } 6\qquad \mathrm{(E) \ } 9 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 11|Solution]]<br />
<br />
== Problem 12 ==<br />
The lines <math> x=\frac{1}{4}y+a </math> and <math> y=\frac{1}{4}x+b </math> intersect at the point <math> (1,2) </math>. What is <math> a+b </math>?<br />
<br />
<math> \mathrm{(A) \ } 0\qquad \mathrm{(B) \ } \frac{3}{4}\qquad \mathrm{(C) \ } 1\qquad \mathrm{(D) \ } 2\qquad \mathrm{(E) \ } \frac{9}{4} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 12|Solution]]<br />
<br />
== Problem 13 ==<br />
Joe and JoAnn each bought 12 ounces of coffee in a 16 ounce cup. Joe drank 2 ounces of his coffee and then added 2 ounces of cream. JoAnn added 2 ounces of cream, stirred the coffee well, and then drank 2 ounces. What is the resulting ratio of the amount of cream in Joe's coffee to that in JoAnn's coffee? <br />
<br />
<math> \mathrm{(A) \ } \frac{6}{7}\qquad \mathrm{(B) \ } \frac{13}{14}\qquad \mathrm{(C) \ }1 \qquad \mathrm{(D) \ } \frac{14}{13}\qquad \mathrm{(E) \ } \frac{7}{6} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 13|Solution]]<br />
<br />
== Problem 14 ==<br />
Let <math>a</math> and <math>b</math> be the roots of the equation <math> x^2-mx+2=0 </math>. Suppose that <math> a+(1/b) </math> and <math> b+(1/a) </math> are the roots of the equation <math> x^2-px+q=0 </math>. What is <math>q</math>?<br />
<br />
<math> \mathrm{(A) \ } \frac{5}{2}\qquad \mathrm{(B) \ } \frac{7}{2}\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } \frac{9}{2}\qquad \mathrm{(E) \ } 8 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 14|Solution]]<br />
<br />
== Problem 15 ==<br />
Rhombus <math>ABCD</math> is similar to rhombus <math>BFDE</math>. The area of rhombus <math>ABCD</math> is <math>24</math> and <math> \angle BAD = 60^\circ </math>. What is the area of rhombus <math>BFDE</math>? <br />
<br />
<asy><br />
unitsize(3cm);<br />
defaultpen(.8);<br />
<br />
pair A=(0,0), B=(1,0), D=dir(60), C=B+D;<br />
<br />
draw(A--B--C--D--cycle);<br />
pair Ep = intersectionpoint( B -- (B+10*dir(150)), D -- (D+10*dir(270)) );<br />
pair F = intersectionpoint( B -- (B+10*dir(90)), D -- (D+10*dir(330)) );<br />
<br />
draw(B--Ep--D--F--cycle);<br />
<br />
label("$A$",A,SW);<br />
label("$B$",B,SE);<br />
label("$C$",C,NE);<br />
label("$D$",D,NW);<br />
label("$E$",Ep,SW);<br />
label("$F$",F,NE);<br />
</asy><br />
<br />
<math> \mathrm{(A) \ } 6\qquad \mathrm{(B) \ } 4\sqrt{3}\qquad \mathrm{(C) \ } 8\qquad \mathrm{(D) \ } 9\qquad \mathrm{(E) \ } 6\sqrt{3} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 15|Solution]]<br />
<br />
== Problem 16 ==<br />
Leap Day, February 29, 2004, occurred on a Sunday. On what day of the week will Leap Day, February 29, 2020, occur? <br />
<br />
<math> \mathrm{(A) \ } \textrm{Tuesday} \qquad \mathrm{(B) \ } \textrm{Wednesday} \qquad \mathrm{(C) \ } \textrm{Thursday} \qquad \mathrm{(D) \ } \textrm{Friday} \qquad \mathrm{(E) \ } \textrm{Saturday} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 16|Solution]]<br />
<br />
== Problem 17 ==<br />
Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob's bag. Bob then randomly selects one ball from his bag and puts it into Alice's bag. What is the probability that after this process the contents of the two bags are the same? <br />
<br />
<math> \mathrm{(A) \ } \frac{1}{10}\qquad \mathrm{(B) \ } \frac{1}{6}\qquad \mathrm{(C) \ } \frac{1}{5}\qquad \mathrm{(D) \ } \frac{1}{3}\qquad \mathrm{(E) \ } \frac{1}{2} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 17|Solution]]<br />
<br />
== Problem 18 ==<br />
Let <math> a_1 , a_2 , ... </math> be a sequence for which<br />
<br />
<math> a_1=2 </math> , <math> a_2=3 </math>, and <math>a_n=\frac{a_{n-1}}{a_{n-2}} </math> for each positive integer <math> n \ge 3 </math>. <br />
<br />
What is <math> a_{2006} </math>?<br />
<br />
<math> \mathrm{(A) \ } \frac{1}{2}\qquad \mathrm{(B) \ } \frac{2}{3}\qquad \mathrm{(C) \ } \frac{3}{2}\qquad \mathrm{(D) \ } 2\qquad \mathrm{(E) \ } 3 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 18|Solution]]<br />
<br />
== Problem 19 ==<br />
A circle of radius <math>2</math> is centered at <math>O</math>. Square <math>OABC</math> has side length <math>1</math>. Sides <math>AB</math> and <math>CB</math> are extended past <math>B</math> to meet the circle at <math>D</math> and <math>E</math>, respectively. What is the area of the shaded region in the figure, which is bounded by <math>BD</math>, <math>BE</math>, and the minor arc connecting <math>D</math> and <math>E</math>?<br />
<br />
<asy><br />
unitsize(1.5cm);<br />
defaultpen(.8);<br />
<br />
draw( circle( (0,0), 2 ) );<br />
draw( (-2,0) -- (2,0) );<br />
draw( (0,-2) -- (0,2) );<br />
<br />
pair D = intersectionpoint( circle( (0,0), 2 ), (1,0) -- (1,2) );<br />
pair Ep = intersectionpoint( circle( (0,0), 2 ), (0,1) -- (2,1) );<br />
draw( (1,0) -- D );<br />
draw( (0,1) -- Ep );<br />
<br />
filldraw( (1,1) -- arc( (0,0),Ep,D ) -- cycle, mediumgray, black );<br />
<br />
label("$O$",(0,0),SW);<br />
label("$A$",(1,0),S);<br />
label("$C$",(0,1),W);<br />
label("$B$",(1,1),SW);<br />
label("$D$",D,N);<br />
label("$E$",Ep,E);<br />
</asy><br />
<br />
<math> \mathrm{(A) \ } \frac{\pi}{3}+1-\sqrt{3}\qquad \mathrm{(B) \ } \frac{\pi}{2}(2-\sqrt{3})\qquad \mathrm{(C) \ } \pi(2-\sqrt{3})\qquad \mathrm{(D) \ } \frac{\pi}{6}+\frac{\sqrt{3}+1}{2}\qquad \mathrm{(E) \ } \frac{\pi}{3}-1+\sqrt{3} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 19|Solution]]<br />
<br />
== Problem 20 ==<br />
In rectangle <math>ABCD</math>, we have <math>A=(6,-22)</math>, <math>B=(2006,178)</math>, <math>D=(8,y)</math>, for some integer <math>y</math>. What is the area of rectangle <math>ABCD</math>?<br />
<br />
<math> \mathrm{(A) \ } 4000\qquad \mathrm{(B) \ } 4040\qquad \mathrm{(C) \ } 4400\qquad \mathrm{(D) \ } 40,000\qquad \mathrm{(E) \ } 40,400 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 20|Solution]]<br />
<br />
== Problem 21 ==<br />
For a particular peculiar pair of dice, the probabilities of rolling <math>1</math>, <math>2</math>, <math>3</math>, <math>4</math>, <math>5</math>, and <math>6</math>, on each die are in the ratio <math>1:2:3:4:5:6</math>. What is the probability of rolling a total of <math>7</math> on the two dice? <br />
<br />
<math> \mathrm{(A) \ } \frac{4}{63}\qquad \mathrm{(B) \ } \frac{1}{8}\qquad \mathrm{(C) \ } \frac{8}{63}\qquad \mathrm{(D) \ } \frac{1}{6}\qquad \mathrm{(E) \ } \frac{2}{7} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 21|Solution]]<br />
<br />
== Problem 22 ==<br />
Elmo makes <math>N</math> sandwiches for a fundraiser. For each sandwich he uses <math>B</math> globs of peanut butter at <math>4\cent</math> per glob and <math>J</math> blobs of jam at <math>5\cent</math> per blob. The cost of the peanut butter and jam to make all the sandwiches is <math>\$2.53</math>. Assume that <math>B</math>, <math>J</math>, and <math>N</math> are positive integers with <math>N>1</math>. What is the cost of the jam Elmo uses to make the sandwiches?<br />
<br />
<math> \mathrm{(A) \ } 1.05\qquad \mathrm{(B) \ } 1.25\qquad \mathrm{(C) \ } 1.45\qquad \mathrm{(D) \ } 1.65\qquad \mathrm{(E) \ } 1.85 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 22|Solution]]<br />
<br />
== Problem 23 ==<br />
A triangle is partitioned into three triangles and a quadrilateral by drawing two lines from vertices to their opposite sides. The areas of the three triangles are 3, 7, and 7 as shown. What is the area of the shaded quadrilateral?<br />
<br />
<asy><br />
unitsize(1.5cm);<br />
defaultpen(.8);<br />
<br />
pair A = (0,0), B = (3,0), C = (1.4, 2), D = B + 0.4*(C-B), Ep = A + 0.3*(C-A);<br />
pair F = intersectionpoint( A--D, B--Ep );<br />
<br />
draw( A -- B -- C -- cycle );<br />
draw( A -- D );<br />
draw( B -- Ep );<br />
filldraw( D -- F -- Ep -- C -- cycle, mediumgray, black );<br />
<br />
label("$7$",(1.25,0.2));<br />
label("$7$",(2.2,0.45));<br />
label("$3$",(0.45,0.35));<br />
</asy><br />
<br />
<math> \mathrm{(A) \ } 15\qquad \mathrm{(B) \ } 17\qquad \mathrm{(C) \ } \frac{35}{2}\qquad \mathrm{(D) \ } 18\qquad \mathrm{(E) \ } \frac{55}{3} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 23|Solution]]<br />
<br />
== Problem 24 ==<br />
Circles with centers <math>O</math> and <math>P</math> have radii <math>2</math> and <math>4</math>, respectively, and are externally tangent. Points <math>A</math> and <math>B</math> on the circle with center <math>O</math> and points <math>C</math> and <math>D</math> on the circle with center <math>P</math> are such that <math>AD</math> and <math>BC</math> are common external tangents to the circles. What is the area of the concave hexagon <math>AOBCPD</math>?<br />
<br />
<asy><br />
unitsize(.7cm);<br />
defaultpen(.8);<br />
<br />
pair O = (0,0), P = (6,0), Q = (-6,0);<br />
pair A = intersectionpoint( arc( (-3,0), (0,0), (-6,0) ), circle( O, 2 ) );<br />
pair B = (A.x, -A.y );<br />
pair D = Q + 2*(A-Q);<br />
pair C = Q + 2*(B-Q);<br />
<br />
draw( circle(O,2) );<br />
draw( circle(P,4) );<br />
draw( (Q + 0.8*(A-Q)) -- ( Q + 2.3*(A-Q) ) );<br />
draw( (Q + 0.8*(B-Q)) -- ( Q + 2.3*(B-Q) ) );<br />
draw( A -- O -- B );<br />
draw( C -- P -- D );<br />
draw( O -- P );<br />
<br />
label("$O$",O,W);<br />
label("$P$",P,E);<br />
<br />
label("$A$",A,NNW);<br />
label("$B$",B,SSW);<br />
<br />
label("$D$",D,NNW);<br />
label("$C$",C,SSW);<br />
</asy><br />
<br />
<math> \mathrm{(A) \ } 18\sqrt{3}\qquad \mathrm{(B) \ } 24\sqrt{2}\qquad \mathrm{(C) \ } 36\qquad \mathrm{(D) \ } 24\sqrt{3}\qquad \mathrm{(E) \ } 32\sqrt{2} </math><br />
<br />
[[2006 AMC 10B Problems/Problem 24|Solution]]<br />
<br />
== Problem 25 ==<br />
Mr. Jones has eight children of different ages. On a family trip his oldest child, who is 9, spots a license plate with a 4-digit number in which each of two digits appears two times. "Look, daddy!" she exclaims. "That number is evenly divisible by the age of each of us kids!" "That's right," replies Mr. Jones, "and the last two digits just happen to be my age." Which of the following is <b><i>not</i></b> the age of one of Mr. Jones's children? <br />
<br />
<math> \mathrm{(A) \ } 4\qquad \mathrm{(B) \ } 5\qquad \mathrm{(C) \ } 6\qquad \mathrm{(D) \ } 7\qquad \mathrm{(E) \ } 8 </math><br />
<br />
[[2006 AMC 10B Problems/Problem 25|Solution]]<br />
<br />
== See also ==<br />
{{AMC10 box|year=2006|ab=A|before=[[2006 AMC 10A Problems]]|after=[[2007 AMC 10A Problems]]}}<br />
* [[AMC 10]]<br />
* [[AMC 10 Problems and Solutions]]<br />
* [[2006 AMC 10B]]<br />
* [https://artofproblemsolving.com/school/mathjams-transcripts?id=143 2006 AMC B Math Jam Transcript]<br />
* [[Mathematics competition resources]]<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Chicken_McNugget_Theorem&diff=86363Chicken McNugget Theorem2017-07-13T18:51:46Z<p>Bluecarneal: /* Problems */</p>
<hr />
<div>The '''Chicken McNugget Theorem''' (or '''Postage Stamp Problem''' or '''Frobenius Coin Problem''') states that for any two [[relatively prime]] [[positive integer]]s <math>m,n</math>, the greatest integer that cannot be written in the form <math>am + bn</math> for [[nonnegative]] integers <math>a, b</math> is <math>mn-m-n</math>.<br />
<br />
A consequence of the theorem is that there are exactly <math>\frac{(m - 1)(n - 1)}{2}</math> positive integers which cannot be expressed in the form <math>am + bn</math>. The proof is based on the fact that in each pair of the form <math>(k, (m - 1)(n - 1) - k+1)</math>, exactly one element is expressible.<br />
<br />
== Origins ==<br />
There are many stories surrounding the origin of the Chicken McNugget theorem. However, the most popular by far remains that of the Chicken McNugget. Originally, McDonald's sold its nuggets in packs of 9 and 20. Math enthusiasts were curious to find the largest number of nuggets that could not have been bought with these packs, thus creating the Chicken McNugget Theorem (the answer worked out to be 151 nuggets). The Chicken McNugget Theorem has also been called the Frobenius Coin Problem or the Frobenius Problem, after German mathematician Ferdinand Frobenius inquired about the largest amount of currency that could not have been made with certain types of coins.<br />
<br />
<br />
<br />
<br />
<br />
==Proof 1==<br />
<b>Definition</b>. An integer <math>N \in \mathbb{Z}</math> will be called <i>purchasable</i> if there exist nonnegative integers <math>a,b</math> such that <math>am+bn = N</math>.<br />
<br />
We would like to prove that <math>mn-m-n</math> is the largest non-purchasable integer. We are required to show that (1) <math>mn-m-n</math> is non-purchasable, and (2) every <math>N > mn-m-n</math> is purchasable. <br />
Note that all purchasable integers are nonnegative, thus the set of non-purchasable integers is nonempty.<br />
<br />
<b>Lemma</b>. Let <math>A_{N} \subset \mathbb{Z} \times \mathbb{Z}</math> be the set of solutions <math>(x,y)</math> to <math>xm+yn = N</math>. Then <math>A_{N} = \{(x+kn,y-km) \;:\; k \in \mathbb{Z}\}</math> for any <math>(x,y) \in A_{N}</math>.<br />
<br />
<i>Proof</i>: By [[Bezout's Lemma]], there exist integers <math>x',y'</math> such that <math>x'm+y'n = 1</math>. Then <math>(Nx')m+(Ny')n = N</math>. Hence <math>A_{N}</math> is nonempty. It is easy to check that <math>(Nx'+kn,Ny'-km) \in A_{N}</math> for all <math>k \in \mathbb{Z}</math>. We now prove that there are no others. Suppose <math>(x_{1},y_{1})</math> and <math>(x_{2},y_{2})</math> are solutions to <math>xm+yn=N</math>. Then <math>x_{1}m+y_{1}n = x_{2}m+y_{2}n</math> implies <math>m(x_{1}-x_{2}) = n(y_{2}-y_{1})</math>. Since <math>m</math> and <math>n</math> are coprime and <math>m</math> divides <math>n(y_{2}-y_{1})</math>, <math>m</math> divides <math>y_{2}-y_{1}</math> and <math>y_{2} \equiv y_{1} \pmod{m}</math>. Similarly <math>x_{2} \equiv x_{1} \pmod{n}</math>. Let <math>k_{1},k_{2}</math> be integers such that <math>x_{2}-x_{1} = k_{1}n</math> and <math>y_{2}-y_{1} = k_{2}m</math>. Then <math>m(-k_{1}n) = n(k_{2}m)</math> implies <math>k_{1} = -k_{2}.</math> We have the desired result. <math>\square</math><br />
<br />
<b>Lemma</b>. For any integer <math>N</math>, there exists unique <math>(a_{N},b_{N}) \in \mathbb{Z} \times \{0,1,\ldots,m-1\}</math> such that <math>a_{N}m + b_{N}n = N</math>.<br />
<br />
<i>Proof</i>: By the division algorithm, there exists <math>k</math> such that <math>0 \le y-km \le m-1</math>. <math>\square</math><br />
<br />
<b>Lemma</b>. <math>N</math> is purchasable if and only if <math>a_{N} \ge 0</math>.<br />
<br />
<i>Proof</i>: If <math>a_{N} \ge 0</math>, then we may simply pick <math>(a,b) = (a_{N},b_{N})</math> so <math>N</math> is purchasable. If <math>a_{N} < 0</math>, then <math>a_{N}+kn < 0</math> if <math>k \le 0</math> and <math>b_{N}-km < 0</math> if <math>k > 0</math>, hence at least one coordinate of <math>(a_{N}+kn,b_{N}-km)</math> is negative for all <math>k \in \mathbb{Z}</math>. Thus <math>N</math> is not purchasable. <math>\square</math><br />
<br />
Thus the set of non-purchasable integers is <math>\{xm+yn \;:\; x<0,0 \le y \le m-1\}</math>. We would like to find the maximum of this set. <br />
Since both <math>m,n</math> are positive, the maximum is achieved when <math>x = -1</math> and <math>y = m-1</math> so that <math>xm+yn = (-1)m+(m-1)n = mn-m-n</math>.<br />
<br />
==Proof 2==<br />
We start with this statement taken from [[Fermat%27s_Little_Theorem#Proof_2_.28Inverses.29|Proof 2 of Fermat's Little Theorem]]:<br />
<br />
"Let <math>S = \{1,2,3,\cdots, p-1\}</math>. Then, we claim that the set <math>a \cdot S</math>, consisting of the product of the elements of <math>S</math> with <math>a</math>, taken modulo <math>p</math>, is simply a permutation of <math>S</math>. In other words, <br />
<br />
<center><cmath>S \equiv \{1a, 2a, \cdots, (p-1)a\} \pmod{p}.</cmath></center><br><br />
<br />
Clearly none of the <math>ia</math> for <math>1 \le i \le p-1</math> are divisible by <math>p</math>, so it suffices to show that all of the elements in <math>a \cdot S</math> are distinct. Suppose that <math>ai \equiv aj \pmod{p}</math> for <math>i \neq j</math>. Since <math>\text{gcd}\, (a,p) = 1</math>, by the cancellation rule, that reduces to <math>i \equiv j \pmod{p}</math>, which is a contradiction."<br />
<br />
Because <math>m</math> and <math>n</math> are coprime, we know that multiplying the residues of <math>m</math> by <math>n</math> simply permutes these residues. Each of these permuted residues is purchasable (using the definition from Proof 1), because, in the form <math>am+bn</math>, <math>a</math> is <math>0</math> and <math>b</math> is the original residue. We now prove the following lemma.<br />
<br />
<b>Lemma</b>: For any nonnegative integer <math>c < m</math>, <math>cn</math> is the least purchasable number <math>\equiv cn \bmod m</math>.<br />
<br />
<i>Proof</i>: Any number that is less than <math>cn</math> and congruent to it <math>\bmod m</math> can be represented in the form <math>cn-dm</math>, where <math>d</math> is a positive integer. If this is purchasable, we can say <math>cn-dm=am+bn</math> for some nonnegative integers <math>a, b</math>. This can be rearranged into <math>(a+d)m=(c-b)n</math>, which implies that <math>(a+d)</math> is a multiple of <math>n</math> (since <math>\gcd(m, n)=1</math>). We can say that <math>(a+d)=gn</math> for some positive integer <math>g</math>, and substitute to get <math>gmn=(c-b)n</math>. Because <math>c < m</math>, <math>(c-b)n < mn</math>, and <math>gmn < mn</math>. We divide by <math>mn</math> to get <math>g<1</math>. However, we defined <math>g</math> to be a positive integer, and all positive integers are greater than or equal to <math>1</math>. Therefore, we have a contradiction, and <math>cn</math> is the least purchasable number congruent to <math>cn \bmod m</math>. <math>\square</math><br />
<br />
This means that because <math>cn</math> is purchasable, every number that is greater than <math>cn</math> and congruent to it <math>\bmod m</math> is also purchasable (because these numbers are in the form <math>am+bn</math> where <math>b=c</math>). Another result of this Lemma is that <math>cn-m</math> is the greatest number <math>\equiv cn \bmod m</math> that is not purchasable. <math>c \leq m-1</math>, so <math>cn-m \leq (m-1)n-m=mn-m-n</math>, which shows that <math>mn-m-n</math> is the greatest number in the form <math>cn-m</math>. Any number greater than this and congruent to some <math>cn \bmod m</math> is purchasable, because that number is greater than <math>cn</math>. All numbers are congruent to some <math>cn</math>, and thus all numbers greater than <math>mn-m-n</math> are purchasable.<br />
<br />
Putting it all together, we can say that for any coprime <math>m</math> and <math>n</math>, <math>mn-m-n</math> is the greatest number not representable in the form <math>am + bn</math> for nonnegative integers <math>a, b</math>. <math>\square</math><br />
<br />
==Corollary==<br />
This corollary is based off of Proof 2, so it is necessary to read that proof before this corollary. We prove the following lemma.<br />
<br />
<b>Lemma</b> For any integer <math>k</math>, exactly one of the integers <math>k</math>, <math>mn-m-n-k</math> is not purchasable.<br />
<br />
<i>Proof</i>: Because every number is congruent to some residue of <math>m</math> permuted by <math>n</math>, we can set <math>k \equiv cn \bmod m</math> for some <math>c</math>. We can break this into two cases.<br />
<br />
<i>Case 1</i>: <math>k \leq cn-m</math>. This implies that <math>k</math> is not purchasable, and that <math>mn-m-n-k \geq mn-m-n-(cn-m) = n(m-1-c)</math>. <math>n(m-1-c)</math> is a permuted residue, and a result of the lemma in Proof 2 was that a permuted residue is the least number congruent to itself <math>\bmod m</math> that is purchasable. Therefore, <math>mn-m-n-k \equiv n(m-1-c) \bmod m</math> and <math>mn-m-n-k \geq n(m-1-c)</math>, so <math>mn-m-n-k</math> is purchasable.<br />
<br />
<i>Case 2</i>: <math>k > cn-m</math>. This implies that <math>k</math> is purchasable, and that <math>mn-m-n-k < mn-m-n-(cn-m) = n(m-1-c)</math>. Again, because <math>n(m-1-c)</math> is the least number congruent to itself <math>\bmod m</math> that is purchasable, and because <math>mn-m-n-k \equiv n(m-1-c) \bmod m</math> and <math>mn-m-n-k < n(m-1-c)</math>, <math>mn-m-n-k</math> is not purchasable.<br />
<br />
We now limit the values of <math>k</math> to all integers <math>0 \leq k \leq \frac{mn-m-n}{2}</math>, which limits the values of <math>mn-m-n-k</math> to <math>mn-m-n \geq mn-m-n-k \geq \frac{mn-m-n}{2}</math>. Because <math>m</math> and <math>n</math> are coprime, only one of them can be a multiple of <math>2</math>. Therefore, <math>mn-m-n \equiv (0)(1)-0-1 \equiv -1 \equiv 1 \bmod 2</math>, showing that <math>\frac{mn-m-n}{2}</math> is not an integer and that <math>\frac{mn-m-n-1}{2}</math> and <math>\frac{mn-m-n+1}{2}</math> are integers. We can now set limits that are equivalent to the previous on the values of <math>k</math> and <math>mn-m-n-k</math> so that they cover all integers form <math>0</math> to <math>mn-m-n</math> without overlap: <math>0 \leq k \leq \frac{mn-m-n-1}{2}</math> and <math>\frac{mn-m-n+1}{2} \leq mn-m-n-k \leq mn-m-n</math>. There are <math>\frac{mn-m-n-1}{2}+1=\frac{(m-1)(n-1)}{2}</math> values of <math>k</math>, and each is paired with a value of <math>mn-m-n-k</math>, so we can make <math>\frac{(m-1)(n-1)}{2}</math> different ordered pairs of the form <math>(k, mn-m-n-k)</math>. The coordinates of these ordered pairs cover all integers from <math>0</math> to <math>mn-m-n</math> inclusive, and each contains exactly one not-purchasable integer, so that means that there are <math>\frac{(m-1)(n-1)}{2}</math> different not-purchasable integers from <math>0</math> to <math>mn-m-n</math>. All integers greater than <math>mn-m-n</math> are purchasable, so that means there are a total of <math>\frac{(m-1)(n-1)}{2}</math> integers <math>\geq 0</math> that are not purchasable.<br />
<br />
In other words, for every pair of coprime integers <math>m, n</math>, there are exactly <math>\frac{(m-1)(n-1)}{2}</math> nonnegative integers that cannot be represented in the form <math>am + bn</math> for nonnegative integers <math>a, b</math>. <math>\square</math><br />
<br />
==Generalization==<br />
If <math>m</math> and <math>n</math> are not coprime, then we can simply rearrange <math>am+bn</math> into the form<br />
<cmath>\gcd(m,n) \left( a\frac{m}{\gcd(m,n)}+b\frac{n}{\gcd(m,n)} \right)</cmath><br />
<math>\frac{m}{\gcd(m,n)}</math> and <math>\frac{n}{\gcd(m,n)}</math> are coprime, so we apply Chicken McNugget to find a bound<br />
<cmath>\frac{mn}{\gcd(m,n)^{2}}-\frac{m}{\gcd(m,n)}-\frac{n}{\gcd(m,n)}</cmath><br />
We can simply multiply <math>\gcd(m,n)</math> back into the bound to get<br />
<cmath>\frac{mn}{\gcd(m,n)}-m-n=\textrm{lcm}(m, n)-m-n</cmath><br />
Therefore, all multiples of <math>\gcd(m, n)</math> greater than <math>\textrm{lcm}(m, n)-m-n</math> are representable in the form <math>am+bn</math> for some positive integers <math>a, b</math>.<br />
<br />
=Problems=<br />
<br />
===Simple===<br />
*Marcy buys paint jars in containers of <math>2</math> and <math>7</math>. What's the largest number of paint jars that Marcy can't obtain? <br />
<br />
Answer: <math>5</math> containers<br />
<br />
*Bay Area Rapid food sells chicken nuggets. You can buy packages of <math>11</math> or <math>7</math>. What is the largest integer <math>n</math> such that there is no way to buy exactly <math>n</math> nuggets? Can you Generalize ?(ACOPS) <br />
<br />
Answer: <math>59</math> dollars<br />
<br />
*If a game of American Football has only scores of field goals (3 points) and touchdowns with the extra point (7 points), then what is the greatest score that cannot be the score of a team in this football game (ignoring time constraints)?<br />
<br />
Answer: <math>11</math> points<br />
<br />
===Intermediate===<br />
*Ninety-four bricks, each measuring <math>4''\times10''\times19'',</math> are to stacked one on top of another to form a tower 94 bricks tall. Each brick can be oriented so it contributes <math>4''\,</math> or <math>10''\,</math> or <math>19''\,</math> to the total height of the tower. How many different tower heights can be achieved using all ninety-four of the bricks? [[1994 AIME Problems/Problem 11|AIME]]<br />
<br />
===Olympiad===<br />
*On the real number line, paint red all points that correspond to integers of the form <math>81x+100y</math>, where <math>x</math> and <math>y</math> are positive integers. Paint the remaining integer point blue. Find a point <math>P</math> on the line such that, for every integer point <math>T</math>, the reflection of <math>T</math> with respect to <math>P</math> is an integer point of a different colour than <math>T</math>. (India TST)<br />
<br />
*Let <math>S</math> be a set of integers (not necessarily positive) such that<br />
<br />
(a) there exist <math>a,b \in S</math> with <math>\gcd(a,b)=\gcd(a-2,b-2)=1</math>;<br />
<br />
(b) if <math>x</math> and <math>y</math> are elements of <math>S</math> (possibly equal), then <math>x^2-y</math> also belongs to <math>S</math>. <br />
<br />
Prove that <math>S</math> is the set of all integers. (USAMO)<br />
<br />
==See Also==<br />
*[[Theorem]]<br />
*[[Prime]]<br />
<br />
[[Category:Theorems]]<br />
[[Category:Number theory]]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Gmaas&diff=78698Gmaas2016-05-24T17:56:57Z<p>Bluecarneal: /* Known Facts About gmaas */</p>
<hr />
<div>=== Known Facts About gmaas ===<br />
<br />
- gmaas is 5space's favorite animal. [http://artofproblemsolving.com/wiki/index.php?title=File:Gmaas2.png (Source)]<br />
<br />
- He lives with sseraj. <br />
<br />
- He is often malnourished by sseraj.<br />
<br />
- He is an employee of AoPS, but doesn't teach. His sole purpose (in life) is to scare people.<br />
<br />
- He is a gmaas with white fur and yellow hypnotizing eyes.<br />
<br />
- He was born with a tail that is a completely different color from the rest of his fur.<br />
<br />
- His stare is not as effective at getting table scraps as Gizmo's stare is, but it is still very hypnotizing.<br />
<br />
- He sometimes appears about half an hour before certain classes as an admin for just a few minutes, such as Alligator Swamp B.<br />
<br />
- He almost died from a lot of Rubik's cubes in an Alligator Swamp A class<br />
<br />
- It is uncertain whether or not he is a cat, or is merely some sort of beast that has chosen to take the form of a cat (specifically a Persian Smoke.) <br />
<br />
- He is very famous now, and mods always talk about him before class starts.<br />
<br />
- Gmaas sightings are not very common. There have only been 7 confirmed sightings of gmaas in the wild.<br />
<br />
- Places where gmaas sightings have happened: <br />
~MouseFeastForCats/CAT 8 Mouse Apartment 1083<br />
~Alligator Swamp A 1072 <br />
~Alligator Swamp B 1073<br />
~Welcome to Panda Town Gate 1076<br />
~Welcome to Gmaas Town Gate 1221<br />
~Welcome to Gmaas Town Gate 1125<br />
~33Â°01'17.4"N 117Â°05'40.1"W<br />
<br />
- These have all been designated as the most glorious sections of Aopsland now, but deforestation threatens the wild areas (eg. Alligator Swamps A&B).<br />
<br />
- If you make yourself more than just a cat... if you devote yourself to an ideal... and if they can't stop you... then you become something else entirely. A LEGEND. Gmaas now belongs to the ages.<br />
<br />
=== gmaas in Popular Culture ===<br />
<br />
- Currently, [https://docs.google.com/document/d/1mLa2d_9Qgv4C9cZdThyjA6kSf2ULgwvkVjPVqmsoV2w/edit a book] is being written (by JpusheenS) about the adventures of gmaas. It is aptly titled, "The Adventures of gmaas".</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Remainder_Theorem&diff=74516Remainder Theorem2016-01-13T23:08:57Z<p>Bluecarneal: /* Theorem */</p>
<hr />
<div>=Theorem=<br />
The Remainder Theorem states that the remainder when the polynomial <math>P(x)</math> is divided by <math>x-a</math> (usually with synthetic division) is equal to the simplified value of <math>P(a)</math><br />
<br />
=Examples=<br />
==Example 1==<br />
What is the remainder in <math>\frac{x^2+2x+3}{x+1}</math>? <br />
==Solution==<br />
Using synthetic or long division we obtain the quotient <math>x+1+\frac{2}{x^2+2x+3}</math>. In this case the remainder is <math>2</math>. However, we could've figured that out by evaluating <math>P(-1)</math>. Remember, we want the divisor in the form of <math>x-a</math>. <math>x+1=x-(-1)</math> so <math>a=-1</math>.<br />
<br />
<math>P(-1) = (-1)^2+2(-1)+3 = 1-2+3 = \boxed{2}</math><br />
<br />
{{stub}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=1986_AHSME_Problems&diff=739301986 AHSME Problems2015-12-25T01:33:03Z<p>Bluecarneal: /* Problem 6 */</p>
<hr />
<div>== Problem 1 ==<br />
<math>[x-(y-x)] - [(x-y) - x] =</math><br />
<br />
<math>\textbf{(A)}\ 2y \qquad<br />
\textbf{(B)}\ 2x \qquad<br />
\textbf{(C)}\ -2y \qquad<br />
\textbf{(D)}\ -2x \qquad<br />
\textbf{(E)}\ 0 </math> <br />
<br />
[[1986 AHSME Problems/Problem 1|Solution]]<br />
<br />
== Problem 2 ==<br />
<br />
If the line <math>L</math> in the <math>xy</math>-plane has half the slope and twice the <math>y</math>-intercept of the line <math>y = \frac{2}{3} x + 4</math>, then an equation for <math>L</math> is:<br />
<br />
<math>\textbf{(A)}\ y = \frac{1}{3} x + 8 \qquad<br />
\textbf{(B)}\ y = \frac{4}{3} x + 2 \qquad<br />
\textbf{(C)}\ y =\frac{1}{3}x+4\qquad\\ <br />
\textbf{(D)}\ y =\frac{4}{3}x+4\qquad<br />
\textbf{(E)}\ y =\frac{1}{3}x+2 </math> <br />
<br />
[[1986 AHSME Problems/Problem 2|Solution]]<br />
<br />
== Problem 3 ==<br />
<br />
<math>\triangle ABC</math> is a right angle at <math>C</math> and <math>\angle A = 20^\circ</math>. If <math>BD</math> (<math>D</math> in <math>\overline{AC}</math>) is the bisector of <math>\angle ABC</math>, then <math>\angle BDC =</math><br />
<br />
<math>\textbf{(A)}\ 40^\circ \qquad<br />
\textbf{(B)}\ 45^\circ \qquad<br />
\textbf{(C)}\ 50^\circ \qquad<br />
\textbf{(D)}\ 55^\circ\qquad<br />
\textbf{(E)}\ 60^\circ</math> <br />
<br />
[[1986 AHSME Problems/Problem 3|Solution]]<br />
<br />
== Problem 4 ==<br />
<br />
Let S be the statement <br />
"If the sum of the digits of the whole number <math>n</math> is divisible by <math>6</math>, then <math>n</math> is divisible by <math>6</math>."<br />
<br />
A value of <math>n</math> which shows <math>S</math> to be false is<br />
<br />
<math>\textbf{(A)}\ 30 \qquad<br />
\textbf{(B)}\ 33 \qquad<br />
\textbf{(C)}\ 40 \qquad<br />
\textbf{(D)}\ 42 \qquad<br />
\textbf{(E)}\ \text{ none of these} </math> <br />
<br />
[[1986 AHSME Problems/Problem 4|Solution]]<br />
<br />
== Problem 5 ==<br />
<br />
Simplify <math>\left(\sqrt[6]{27} - \sqrt{6 \frac{3}{4} }\right)^2</math><br />
<br />
<math>\textbf{(A)}\ \frac{3}{4} \qquad<br />
\textbf{(B)}\ \frac{\sqrt 3}{2} \qquad<br />
\textbf{(C)}\ \frac{3\sqrt 3}{4}\qquad<br />
\textbf{(D)}\ \frac{3}{2}\qquad<br />
\textbf{(E)}\ \frac{3\sqrt 3}{2} </math> <br />
<br />
[[1986 AHSME Problems/Problem 5|Solution]]<br />
<br />
== Problem 6 ==<br />
<br />
Using a table of a certain height, two identical blocks of wood are placed as shown in Figure 1. Length <math>r</math> is found to be <math>32</math> inches. After rearranging the blocks as in Figure 2, length <math>s</math> is found to be <math>28</math> inches. How high is the table?<br />
<br />
<asy><br />
size(300);<br />
defaultpen(linewidth(0.8)+fontsize(13pt));<br />
path table = origin--(1,0)--(1,6)--(6,6)--(6,0)--(7,0)--(7,7)--(0,7)--cycle;<br />
path block = origin--(3,0)--(3,1.5)--(0,1.5)--cycle;<br />
path rotblock = origin--(1.5,0)--(1.5,3)--(0,3)--cycle;<br />
draw(table^^shift((14,0))*table);<br />
filldraw(shift((7,0))*block^^shift((5.5,7))*rotblock^^shift((21,0))*rotblock^^shift((18,7))*block,gray);<br />
draw((7.25,1.75)--(8.5,3.5)--(8.5,8)--(7.25,9.75),Arrows(size=5));<br />
draw((21.25,3.25)--(22,3.5)--(22,8)--(21.25,8.25),Arrows(size=5));<br />
unfill((8,5)--(8,6.5)--(9,6.5)--(9,5)--cycle);<br />
unfill((21.5,5)--(21.5,6.5)--(23,6.5)--(23,5)--cycle);<br />
label("$r$",(8.5,5.75));<br />
label("$s$",(22,5.75));<br />
</asy><br />
<br />
<math>\textbf{(A) }28\text{ inches}\qquad\textbf{(B) }29\text{ inches}\qquad\textbf{(C) }30\text{ inches}\qquad\textbf{(D) }31\text{ inches}\qquad\textbf{(E) }32\text{ inches}</math><br />
<br />
[[1986 AHSME Problems/Problem 6|Solution]]<br />
<br />
== Problem 7 ==<br />
<br />
The sum of the greatest integer less than or equal to <math>x</math> and the least integer greater than or equal to <math>x</math> is <math>5</math>. The solution set for <math>x</math> is<br />
<br />
<math>\textbf{(A)}\ \Big\{\frac{5}{2}\Big\}\qquad<br />
\textbf{(B)}\ \big\{x\ |\ 2 \le x \le 3\big\}\qquad<br />
\textbf{(C)}\ \big\{x\ |\ 2\le x < 3\big\}\qquad\\ <br />
\textbf{(D)}\ \Big\{x\ |\ 2 < x\le 3\Big\}\qquad<br />
\textbf{(E)}\ \Big\{x\ |\ 2 < x < 3\Big\} </math><br />
<br />
[[1986 AHSME Problems/Problem 7|Solution]]<br />
<br />
== Problem 8 ==<br />
<br />
The population of the United States in <math>1980</math> was <math>226,504,825</math>. The area of the country is <math>3,615,122</math> square miles. The are <math>(5280)^{2}</math> <br />
square feet in one square mile. Which number below best approximates the average number of square feet per person?<br />
<br />
<math>\textbf{(A)}\ 5,000\qquad<br />
\textbf{(B)}\ 10,000\qquad<br />
\textbf{(C)}\ 50,000\qquad<br />
\textbf{(D)}\ 100,000\qquad<br />
\textbf{(E)}\ 500,000 </math><br />
<br />
[[1986 AHSME Problems/Problem 8|Solution]]<br />
<br />
== Problem 9 ==<br />
<br />
The product <math> \left(1-\frac{1}{2^{2}}\right)\left(1-\frac{1}{3^{2}}\right)\ldots\left(1-\frac{1}{9^{2}}\right)\left(1-\frac{1}{10^{2}}\right)</math> equals<br />
<br />
<math>\textbf{(A)}\ \frac{5}{12}\qquad<br />
\textbf{(B)}\ \frac{1}{2}\qquad<br />
\textbf{(C)}\ \frac{11}{20}\qquad<br />
\textbf{(D)}\ \frac{2}{3}\qquad<br />
\textbf{(E)}\ \frac{7}{10} </math> <br />
<br />
[[1986 AHSME Problems/Problem 9|Solution]]<br />
<br />
== Problem 10 ==<br />
<br />
The <math>120</math> permutations of the <math>AHSME</math> are arranged in dictionary order as if each were an ordinary five-letter word. <br />
The last letter of the <math>85</math>th word in this list is:<br />
<br />
<math>\textbf{(A)}\ \text{A} \qquad<br />
\textbf{(B)}\ \text{H} \qquad<br />
\textbf{(C)}\ \text{S} \qquad<br />
\textbf{(D)}\ \text{M}\qquad<br />
\textbf{(E)}\ \text{E} </math> <br />
<br />
[[1986 AHSME Problems/Problem 10|Solution]]<br />
<br />
== Problem 11 ==<br />
<br />
In <math>\triangle ABC, AB = 13, BC = 14</math> and <math>CA = 15</math>. Also, <math>M</math> is the midpoint of side <math>AB</math> and <math>H</math> is the foot of the altitude from <math>A</math> to <math>BC</math>. <br />
The length of <math>HM</math> is<br />
<br />
<asy><br />
defaultpen(linewidth(0.7)+fontsize(10));<br />
pair H=origin, A=(0,6), B=(-4,0), C=(5,0), M=B+3.6*dir(B--A);<br />
draw(B--C--A--B^^M--H--A^^rightanglemark(A,H,C));<br />
label("A", A, NE);<br />
label("B", B, W);<br />
label("C", C, E);<br />
label("H", H, S);<br />
label("M", M, dir(M));<br />
</asy><br />
<br />
<math>\textbf{(A)}\ 6\qquad<br />
\textbf{(B)}\ 6.5\qquad<br />
\textbf{(C)}\ 7\qquad<br />
\textbf{(D)}\ 7.5\qquad<br />
\textbf{(E)}\ 8 </math><br />
<br />
[[1986 AHSME Problems/Problem 11|Solution]]<br />
<br />
== Problem 12 ==<br />
<br />
John scores <math>93</math> on this year's AHSME. Had the old scoring system still been in effect, he would score only <math>84</math> for the same answers. <br />
How many questions does he leave unanswered? (In the new scoring system one receives <math>5</math> points for correct answers,<br />
<math>0</math> points for wrong answers, and <math>2</math> points for unanswered questions. In the old system, <br />
one started with <math>30</math> points, received <math>4</math> more for each correct answer, <br />
lost one point for each wrong answer, and neither gained nor lost points for unanswered questions. <br />
There are <math>30</math> questions in the <math>1986</math> AHSME.)<br />
<br />
<math>\textbf{(A)}\ 6\qquad<br />
\textbf{(B)}\ 9\qquad<br />
\textbf{(C)}\ 11\qquad<br />
\textbf{(D)}\ 14\qquad<br />
\textbf{(E)}\ \text{Not uniquely determined} </math> <br />
<br />
[[1986 AHSME Problems/Problem 12|Solution]]<br />
<br />
== Problem 13 ==<br />
<br />
A parabola <math>y = ax^{2} + bx + c</math> has vertex <math>(4,2)</math>. If <math>(2,0)</math> is on the parabola, then <math>abc</math> equals<br />
<br />
<math>\textbf{(A)}\ -12\qquad<br />
\textbf{(B)}\ -6\qquad<br />
\textbf{(C)}\ 0\qquad<br />
\textbf{(D)}\ 6\qquad<br />
\textbf{(E)}\ 12 </math><br />
<br />
[[1986 AHSME Problems/Problem 13|Solution]]<br />
<br />
== Problem 14 ==<br />
<br />
Suppose hops, skips and jumps are specific units of length. If <math>b</math> hops equals <math>c</math> skips, <math>d</math> jumps equals <math>e</math> hops, <br />
and <math>f</math>Vjumps equals <math>g</math> meters, then one meter equals how many skips?<br />
<br />
<math>\textbf{(A)}\ \frac{bdg}{cef}\qquad<br />
\textbf{(B)}\ \frac{cdf}{beg}\qquad<br />
\textbf{(C)}\ \frac{cdg}{bef}\qquad<br />
\textbf{(D)}\ \frac{cef}{bdg}\qquad<br />
\textbf{(E)}\ \frac{ceg}{bdf} </math><br />
<br />
[[1986 AHSME Problems/Problem 14|Solution]]<br />
<br />
== Problem 15 ==<br />
<br />
A student attempted to compute the average <math>A</math> of <math>x, y</math> and <math>z</math> by computing the average of <math>x</math> and <math>y</math>, <br />
and then computing the average of the result and <math>z</math>. Whenever <math>x < y < z</math>, the student's final result is<br />
<br />
<math>\textbf{(A)}\ \text{correct}\quad<br />
\textbf{(B)}\ \text{always less than A}\quad<br />
\textbf{(C)}\ \text{always greater than A}\quad\\<br />
\textbf{(D)}\ \text{sometimes less than A and sometimes equal to A}\quad\\<br />
\textbf{(E)}\ \text{sometimes greater than A and sometimes equal to A} \quad </math><br />
<br />
[[1986 AHSME Problems/Problem 15|Solution]]<br />
<br />
== Problem 16 ==<br />
<br />
In <math>\triangle ABC, AB = 8, BC = 7, CA = 6</math> and side <math>BC</math> is extended, as shown in the figure, to a point <math>P</math> so that <math>\triangle PAB</math><br />
is similar to <math>\triangle PCA</math>. The length of <math>PC</math> is<br />
<br />
<asy><br />
defaultpen(linewidth(0.7)+fontsize(10));<br />
pair A=origin, P=(1.5,5), B=(8,0), C=P+2.5*dir(P--B);<br />
draw(A--P--C--A--B--C);<br />
label("A", A, W);<br />
label("B", B, E);<br />
label("C", C, NE);<br />
label("P", P, NW);<br />
label("6", 3*dir(A--C), SE);<br />
label("7", B+3*dir(B--C), NE);<br />
label("8", (4,0), S);<br />
</asy><br />
<br />
<math>\textbf{(A)}\ 7\qquad<br />
\textbf{(B)}\ 8\qquad<br />
\textbf{(C)}\ 9\qquad<br />
\textbf{(D)}\ 10\qquad<br />
\textbf{(E)}\ 11 </math><br />
<br />
[[1986 AHSME Problems/Problem 16|Solution]]<br />
<br />
== Problem 17 ==<br />
<br />
A drawer in a darkened room contains <math>100</math> red socks, <math>80</math> green socks, <math>60</math> blue socks and <math>40</math> black socks. <br />
A youngster selects socks one at a time from the drawer but is unable to see the color of the socks drawn. <br />
What is the smallest number of socks that must be selected to guarantee that the selection contains at least <math>10</math> pairs? <br />
(A pair of socks is two socks of the same color. No sock may be counted in more than one pair.)<br />
<br />
<math>\textbf{(A)}\ 21\qquad<br />
\textbf{(B)}\ 23\qquad<br />
\textbf{(C)}\ 24\qquad<br />
\textbf{(D)}\ 30\qquad<br />
\textbf{(E)}\ 50 </math><br />
<br />
[[1986 AHSME Problems/Problem 17|Solution]]<br />
<br />
== Problem 18 ==<br />
<br />
A plane intersects a right circular cylinder of radius <math>1</math> forming an ellipse. <br />
If the major axis of the ellipse of <math>50\%</math> longer than the minor axis, the length of the major axis is<br />
<br />
<math>\textbf{(A)}\ 1\qquad<br />
\textbf{(B)}\ \frac{3}{2}\qquad<br />
\textbf{(C)}\ 2\qquad<br />
\textbf{(D)}\ \frac{9}{4}\qquad<br />
\textbf{(E)}\ 3 </math> <br />
<br />
[[1986 AHSME Problems/Problem 18|Solution]]<br />
<br />
== Problem 19 ==<br />
<br />
A park is in the shape of a regular hexagon <math>2</math> km on a side. Starting at a corner, <br />
Alice walks along the perimeter of the park for a distance of <math>5</math> km. <br />
How many kilometers is she from her starting point?<br />
<br />
<math>\textbf{(A)}\ \sqrt{13}\qquad<br />
\textbf{(B)}\ \sqrt{14}\qquad<br />
\textbf{(C)}\ \sqrt{15}\qquad<br />
\textbf{(D)}\ \sqrt{16}\qquad<br />
\textbf{(E)}\ \sqrt{17} </math><br />
<br />
[[1986 AHSME Problems/Problem 19|Solution]]<br />
<br />
== Problem 20 ==<br />
<br />
Suppose <math>x</math> and <math>y</math> are inversely proportional and positive. If <math>x</math> increases by <math>p\%</math>, then <math>y</math> decreases by <br />
<br />
<math>\textbf{(A)}\ p\%\qquad<br />
\textbf{(B)}\ \frac{p}{1+p}\%\qquad<br />
\textbf{(C)}\ \frac{100}{p}\%\qquad<br />
\textbf{(D)}\ \frac{p}{100+p}\%\qquad<br />
\textbf{(E)}\ \frac{100p}{100+p}\% </math> <br />
<br />
[[1986 AHSME Problems/Problem 20|Solution]]<br />
<br />
== Problem 21 ==<br />
<br />
In the configuration below, <math>\theta</math> is measured in radians, <math>C</math> is the center of the circle, <br />
<math>BCD</math> and <math>ACE</math> are line segments and <math>AB</math> is tangent to the circle at <math>A</math>.<br />
<br />
<asy><br />
defaultpen(fontsize(10pt)+linewidth(.8pt));<br />
pair A=(0,-1), E=(0,1), C=(0,0), D=dir(10), F=dir(190), B=(-1/sin(10*pi/180))*dir(10);<br />
fill(Arc((0,0),1,10,90)--C--D--cycle,mediumgray);<br />
fill(Arc((0,0),1,190,270)--B--F--cycle,mediumgray);<br />
draw(unitcircle);<br />
draw(A--B--D^^A--E);<br />
label("$A$",A,S);<br />
label("$B$",B,W);<br />
label("$C$",C,SE);<br />
label("$\theta$",C,SW);<br />
label("$D$",D,NE);<br />
label("$E$",E,N);<br />
</asy><br />
<br />
A necessary and sufficient condition for the equality of the two shaded areas, given <math>0 < \theta < \frac{\pi}{2}</math>, is<br />
<br />
<math>\textbf{(A)}\ \tan \theta = \theta\qquad<br />
\textbf{(B)}\ \tan \theta = 2\theta\qquad<br />
\textbf{(C)}\ \tan\theta = 4\theta\qquad<br />
\textbf{(D)}\ \tan 2\theta =\theta\qquad\\ <br />
\textbf{(E)}\ \tan\frac{\theta}{2}=\theta </math> <br />
<br />
[[1986 AHSME Problems/Problem 21|Solution]]<br />
<br />
== Problem 22 ==<br />
<br />
Six distinct integers are picked at random from <math>\{1,2,3,\ldots,10\}</math>. What is the probability that, among those selected, the second smallest is <math>3</math>?<br />
<br />
<math>\textbf{(A)}\ \frac{1}{60}\qquad<br />
\textbf{(B)}\ \frac{1}{6}\qquad<br />
\textbf{(C)}\ \frac{1}{3}\qquad<br />
\textbf{(D)}\ \frac{1}{2}\qquad<br />
\textbf{(E)}\ \text{none of these} </math> <br />
<br />
[[1986 AHSME Problems/Problem 22|Solution]]<br />
<br />
== Problem 23 ==<br />
<br />
Let N = <math>69^{5} + 5*69^{4} + 10*69^{3} + 10*69^{2} + 5*69 + 1</math>. How many positive integers are factors of <math>N</math>?<br />
<br />
<math>\textbf{(A)}\ 3\qquad<br />
\textbf{(B)}\ 5\qquad<br />
\textbf{(C)}\ 69\qquad<br />
\textbf{(D)}\ 125\qquad<br />
\textbf{(E)}\ 216 </math><br />
<br />
[[1986 AHSME Problems/Problem 23|Solution]]<br />
<br />
== Problem 24 ==<br />
<br />
Let <math>p(x) = x^{2} + bx + c</math>, where <math>b</math> and <math>c</math> are integers. <br />
If <math>p(x)</math> is a factor of both <math>x^{4} + 6x^{2} + 25</math> and <math>3x^{4} + 4x^{2} + 28x + 5</math>, what is <math>p(1)</math>?<br />
<br />
<math>\textbf{(A)}\ 0\qquad<br />
\textbf{(B)}\ 1\qquad<br />
\textbf{(C)}\ 2\qquad<br />
\textbf{(D)}\ 4\qquad<br />
\textbf{(E)}\ 8 </math><br />
<br />
[[1986 AHSME Problems/Problem 24|Solution]]<br />
<br />
== Problem 25 ==<br />
<br />
If <math>\lfloor x\rfloor</math> is the greatest integer less than or equal to <math>x</math>, then<br />
<math>\sum_{N=1}^{1024} \lfloor \log_{2}N\rfloor =</math><br />
<br />
<math>\textbf{(A)}\ 8192\qquad<br />
\textbf{(B)}\ 8204\qquad<br />
\textbf{(C)}\ 9218\qquad<br />
\textbf{(D)}\ \lfloor\log_{2}(1024!)\rfloor\qquad<br />
\textbf{(E)}\ \text{none of these} </math> <br />
<br />
[[1986 AHSME Problems/Problem 25|Solution]]<br />
<br />
== Problem 26 ==<br />
<br />
It is desired to construct a right triangle in the coordinate plane so that its legs are parallel <br />
to the <math>x</math> and <math>y</math> axes and so that the medians to the midpoints of the legs lie on the lines <math>y = 3x + 1</math><br />
and <math>y = mx + 2</math>. The number of different constants <math>m</math> for which such a triangle exists is<br />
<br />
<math>\textbf{(A)}\ 0\qquad<br />
\textbf{(B)}\ 1\qquad<br />
\textbf{(C)}\ 2\qquad<br />
\textbf{(D)}\ 3\qquad<br />
\textbf{(E)}\ \text{more than 3} </math> <br />
<br />
[[1986 AHSME Problems/Problem 26|Solution]]<br />
<br />
== Problem 27 ==<br />
<br />
In the adjoining figure, <math>AB</math> is a diameter of the circle, <math>CD</math> is a chord parallel to <math>AB</math>, <br />
and <math>AC</math> intersects <math>BD</math> at <math>E</math>, with <math>\angle AED = \alpha</math>. The ratio of the area of <math>\triangle CDE</math> to that of <math>\triangle ABE</math> is <br />
<br />
<asy><br />
defaultpen(fontsize(10pt)+linewidth(.8pt));<br />
pair A=(-1,0), B=(1,0), E=(0,-.4), C=(.6,-.8), D=(-.6,-.8), E=(0,-.8/(1.6));<br />
draw(unitcircle);<br />
draw(A--B--D--C--A);<br />
draw(Arc(E,.2,155,205));<br />
label("$A$",A,W);<br />
label("$B$",B,C);<br />
label("$C$",C,C);<br />
label("$D$",D,W);<br />
label("$\alpha$",E-(.2,0),W);<br />
label("$E$",E,N);<br />
</asy><br />
<br />
<math>\textbf{(A)}\ \cos\ \alpha\qquad<br />
\textbf{(B)}\ \sin\ \alpha\qquad<br />
\textbf{(C)}\ \cos^2\alpha\qquad<br />
\textbf{(D)}\ \sin^2\alpha\qquad<br />
\textbf{(E)}\ 1-\sin\ \alpha </math><br />
<br />
[[1986 AHSME Problems/Problem 27|Solution]]<br />
<br />
== Problem 28 ==<br />
<br />
<math>ABCDE</math> is a regular pentagon. <math>AP, AQ</math> and <math>AR</math> are the perpendiculars dropped from <math>A</math> onto <math>CD, CB</math> extended and <math>DE</math> extended, <br />
respectively. Let <math>O</math> be the center of the pentagon. If <math>OP = 1</math>, then <math>AO + AQ + AR</math> equals<br />
<br />
<asy><br />
defaultpen(fontsize(10pt)+linewidth(.8pt));<br />
pair O=origin, A=2*dir(90), B=2*dir(18), C=2*dir(306), D=2*dir(234), E=2*dir(162), P=(C+D)/2, Q=C+3.10*dir(C--B), R=D+3.10*dir(D--E), S=C+4.0*dir(C--B), T=D+4.0*dir(D--E);<br />
draw(A--B--C--D--E--A^^E--T^^B--S^^R--A--Q^^A--P^^rightanglemark(A,Q,S)^^rightanglemark(A,R,T));<br />
dot(O);<br />
label("$O$",O,dir(B));<br />
label("$1$",(O+P)/2,W);<br />
label("$A$",A,dir(A));<br />
label("$B$",B,dir(B));<br />
label("$C$",C,dir(C));<br />
label("$D$",D,dir(D));<br />
label("$E$",E,dir(E));<br />
label("$P$",P,dir(P));<br />
label("$Q$",Q,dir(Q));<br />
label("$R$",R,dir(R));<br />
</asy><br />
<br />
<math>\textbf{(A)}\ 3\qquad<br />
\textbf{(B)}\ 1 + \sqrt{5}\qquad<br />
\textbf{(C)}\ 4\qquad<br />
\textbf{(D)}\ 2 + \sqrt{5}\qquad<br />
\textbf{(E)}\ 5 </math> <br />
<br />
[[1986 AHSME Problems/Problem 28|Solution]]<br />
<br />
== Problem 29 ==<br />
<br />
Two of the altitudes of the scalene triangle <math>ABC</math> have length <math>4</math> and <math>12</math>. <br />
If the length of the third altitude is also an integer, what is the biggest it can be?<br />
<br />
<math>\textbf{(A)}\ 4\qquad<br />
\textbf{(B)}\ 5\qquad<br />
\textbf{(C)}\ 6\qquad<br />
\textbf{(D)}\ 7\qquad<br />
\textbf{(E)}\ \text{none of these} </math> <br />
<br />
[[1986 AHSME Problems/Problem 29|Solution]]<br />
<br />
== Problem 30 ==<br />
<br />
The number of real solutions <math>(x,y,z,w)</math> of the simultaneous equations<br />
<math>2y = x + \frac{17}{x}, 2z = y + \frac{17}{y}, 2w = z + \frac{17}{z}, 2x = w + \frac{17}{w}</math><br />
is<br />
<br />
<math>\textbf{(A)}\ 1\qquad<br />
\textbf{(B)}\ 2\qquad<br />
\textbf{(C)}\ 4\qquad<br />
\textbf{(D)}\ 8\qquad<br />
\textbf{(E)}\ 16 </math><br />
<br />
[[1986 AHSME Problems/Problem 30|Solution]]<br />
<br />
== See also ==<br />
* [[AMC 12 Problems and Solutions]]<br />
* [[Mathematics competition resources]]<br />
<br />
{{AHSME box|year=1986|before=[[1985 AHSME]]|after=[[1987 AHSME]]}} <br />
<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=1986_AHSME_Problems/Problem_6&diff=739291986 AHSME Problems/Problem 62015-12-25T01:32:46Z<p>Bluecarneal: /* Problem */</p>
<hr />
<div>==Problem==<br />
Using a table of a certain height, two identical blocks of wood are placed as shown in Figure 1. Length <math>r</math> is found to be <math>32</math> inches. After rearranging the blocks as in Figure 2, length <math>s</math> is found to be <math>28</math> inches. How high is the table?<br />
<br />
<asy><br />
size(300);<br />
defaultpen(linewidth(0.8)+fontsize(13pt));<br />
path table = origin--(1,0)--(1,6)--(6,6)--(6,0)--(7,0)--(7,7)--(0,7)--cycle;<br />
path block = origin--(3,0)--(3,1.5)--(0,1.5)--cycle;<br />
path rotblock = origin--(1.5,0)--(1.5,3)--(0,3)--cycle;<br />
draw(table^^shift((14,0))*table);<br />
filldraw(shift((7,0))*block^^shift((5.5,7))*rotblock^^shift((21,0))*rotblock^^shift((18,7))*block,gray);<br />
draw((7.25,1.75)--(8.5,3.5)--(8.5,8)--(7.25,9.75),Arrows(size=5));<br />
draw((21.25,3.25)--(22,3.5)--(22,8)--(21.25,8.25),Arrows(size=5));<br />
unfill((8,5)--(8,6.5)--(9,6.5)--(9,5)--cycle);<br />
unfill((21.5,5)--(21.5,6.5)--(23,6.5)--(23,5)--cycle);<br />
label("$r$",(8.5,5.75));<br />
label("$s$",(22,5.75));<br />
</asy><br />
<br />
<math>\textbf{(A) }28\text{ inches}\qquad\textbf{(B) }29\text{ inches}\qquad\textbf{(C) }30\text{ inches}\qquad\textbf{(D) }31\text{ inches}\qquad\textbf{(E) }32\text{ inches}</math><br />
<br />
==Solution==<br />
<br />
<br />
== See also ==<br />
{{AHSME box|year=1986|num-b=5|num-a=7}} <br />
<br />
[[Category: Introductory Algebra Problems]]<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2005_AMC_8_Problems/Problem_25&diff=717582005 AMC 8 Problems/Problem 252015-08-24T13:19:34Z<p>Bluecarneal: /* Problem */</p>
<hr />
<div>==Problem==<br />
A square with side length 2 and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?<br />
<br />
<asy>pair a=(4,4), b=(0,0), c=(0,4), d=(4,0), o=(2,2);<br />
draw(a--d--b--c--cycle);<br />
draw(circle(o, 2.5));</asy><br />
<math> \textbf{(A)}\ \frac{2}{\sqrt{\pi}} \qquad \textbf{(B)}\ \frac{1+\sqrt{2}}{2} \qquad \textbf{(C)}\ \frac{3}{2} \qquad \textbf{(D)}\ \sqrt{3} \qquad \textbf{(E)}\ \sqrt{\pi}</math><br />
<br />
==Solution==<br />
<br />
Let the region within the circle and square be <math>a</math>. In other words, it is the intersection of the area of circle and square. Let <math>r</math> be the radius. We know that the area of the circle minus <math>a</math> is equal to the area of the square, minus <math>a</math> . <br />
<br />
We get:<br />
<br />
<math>\pi r^2 -a=4-a</math><br />
<br />
<math>r^2=\frac{4}{\pi}</math><br />
<br />
<math>r=\frac{2}{\sqrt{\pi}}</math><br />
<br />
So the answer is <math>\boxed{\textbf{(A)}\ \frac{2}{\sqrt{\pi}}}</math>.<br />
<br />
==See Also==<br />
{{AMC8 box|year=2005|num-b=24|after=Last <br /> Question}}<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2003_AMC_8_Problems&diff=717572003 AMC 8 Problems2015-08-24T13:18:17Z<p>Bluecarneal: /* Problem 14 */</p>
<hr />
<div>==Problem 1==<br />
Jamie counted the number of edges of a cube, Jimmy counted the numbers of corners, and Judy counted the number of faces. They then added the three numbers. What was the resulting sum? <br />
<br />
<math>\mathrm{(A)}\ 12 \qquad\mathrm{(B)}\ 16 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 22 \qquad\mathrm{(E)}\ 26</math><br />
<br />
[[2003 AMC 8 Problems/Problem 1|Solution]]<br />
<br />
==Problem 2==<br />
Which of the following numbers has the smallest prime factor?<br />
<br />
<math>\mathrm{(A)}\ 55 \qquad\mathrm{(B)}\ 57 \qquad\mathrm{(C)}\ 58 \qquad\mathrm{(D)}\ 59 \qquad\mathrm{(E)}\ 61</math><br />
<br />
[[2003 AMC 8 Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
A burger at Ricky C's weighs 120 grams, of which 30 grams are filler. What percent of the burger is not filler?<br />
<br />
<math>\mathrm{(A)}\ 60\% \qquad\mathrm{(B)}\ 65\% \qquad\mathrm{(C)}\ 70\% \qquad\mathrm{(D)}\ 75\% \qquad\mathrm{(E)}\ 90\%</math><br />
<br />
[[2003 AMC 8 Problems/Problem 3|Solution]]<br />
<br />
==Problem 4==<br />
A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted 7 children and 19 wheels. How many tricycles were there?<br />
<br />
<math>\mathrm{(A)}\ 2 \qquad\mathrm{(B)}\ 4 \qquad\mathrm{(C)}\ 5 \qquad\mathrm{(D)}\ 6 \qquad\mathrm{(E)}\ 7</math><br />
<br />
[[2003 AMC 8 Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
If 20% of a number is 12, what is 30% of the same number?<br />
<br />
<math>\mathrm{(A)}\ 15\qquad\mathrm{(B)}\ 18 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 24 \qquad\mathrm{(E)}\ 30</math><br />
<br />
[[2003 AMC 8 Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
Given the areas of the three squares in the figure, what is the area of the interior triangle?<br />
<br />
<asy><br />
draw((0,0)--(-5,12)--(7,17)--(12,5)--(17,5)--(17,0)--(12,0)--(12,-12)--(0,-12)--(0,0)--(12,5)--(12,0)--cycle,linewidth(1));<br />
label("$25$",(14.5,1),N);<br />
label("$144$",(6,-7.5),N);<br />
label("$169$",(3.5,7),N);<br />
</asy><br />
<br />
<math>\mathrm{(A)}\ 13 \qquad\mathrm{(B)}\ 30 \qquad\mathrm{(C)}\ 60 \qquad\mathrm{(D)}\ 300 \qquad\mathrm{(E)}\ 1800</math><br />
<br />
[[2003 AMC 8 Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jenny's average and Blake's average on these four tests?<br />
<br />
<math> \mathrm{(A)}\ 10 \qquad\mathrm{(B)}\ 15 \qquad\mathrm{(C)}\ 20 \qquad\mathrm{(D)}\ 25 \qquad\mathrm{(E)}\ 40 </math><br />
<br />
[[2003 AMC 8 Problems/Problem 7|Solution]]<br />
<br />
==Bake Sale==<br />
Problems 8, 9, and 10 use the data found in the accompanying paragraph and figures.<br />
<br />
Four friends, Art, Roger, Paul and Trisha, bake cookies, and all cookies have the same thickness. The shapes of the cookies differ, as shown.<br />
<br />
[[File:2003amc8bakesale.png]]<br />
<br />
Each friend uses the same amount of dough, and Art makes exactly 12 cookies. <br />
<br />
===Problem 8===<br />
<br />
Who gets the fewest cookies from one batch of cookie dough?<br />
<br />
<math> \textbf{(A)}\ \text{Art} \qquad\textbf{(B)}\ \text{Paul}\qquad\textbf{(C)}\ \text{Roger}\qquad\textbf{(D)}\ \text{Trisha}\qquad\textbf{(E)}\ \text{There is a tie for fewest.}</math><br />
<br />
[[2003 AMC 8 Problems/Problem 8|Solution]]<br />
<br />
===Problem 9===<br />
<br />
Art's cookies sell for 60 cents each. To earn the same amount from a single batch, how much should one of Roger's cookies cost in cents?<br />
<br />
<math> \textbf{(A)}\ 18\qquad\textbf{(B)}\ 25\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 75\qquad\textbf{(E)}\ 90</math><br />
<br />
[[2003 AMC 8 Problems/Problem 9|Solution]]<br />
<br />
===Problem 10===<br />
<br />
How many cookies will be in one batch of Trisha's cookies?<br />
<br />
<math> \textbf{(A)}\ 10\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 24</math><br />
<br />
[[2003 AMC 8 Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
<br />
Business is a little slow at Lou's Fine Shoes, so Lou decides to have a sale. On Friday, Lou increases all of Thursday's prices by 10%. Over the weekend, Lou advertises the sale: "Ten percent off the listed price. Sale starts Monday." How much does a pair of shoes cost on Monday that cost 40 dollars on Thursday?<br />
<br />
<math> \textbf{(A)}\ 36\qquad\textbf{(B)}\ 39.60\qquad\textbf{(C)}\ 40\qquad\textbf{(D)}\ 40.40\qquad\textbf{(E)}\ 44 </math><br />
<br />
[[2003 AMC 8 Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
<br />
When a fair six-sided die is tossed on a table top, the bottom face cannot be seen. What is the probability that the product of the numbers on the five faces that can be seen is divisible by 6?<br />
<br />
<math> \textbf{(A)}\ \frac{1}{3}\qquad\textbf{(B)}\ \frac{1}{2}\qquad\textbf{(C)}\ \frac{2}{3}\qquad\textbf{(D)}\ \frac{5}{6}\qquad\textbf{(E)}\ 1</math><br />
<br />
[[2003 AMC 8 Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
<br />
Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?<br />
<br />
<asy><br />
import three;<br />
defaultpen(linewidth(0.8));<br />
real r=0.5;<br />
currentprojection=orthographic(3/4,8/15,7/15);<br />
draw(unitcube, white, thick(), nolight);<br />
draw(shift(1,0,0)*unitcube, white, thick(), nolight);<br />
draw(shift(2,0,0)*unitcube, white, thick(), nolight);<br />
draw(shift(0,0,1)*unitcube, white, thick(), nolight);<br />
draw(shift(2,0,1)*unitcube, white, thick(), nolight);<br />
draw(shift(0,1,0)*unitcube, white, thick(), nolight);<br />
draw(shift(2,1,0)*unitcube, white, thick(), nolight);<br />
draw(shift(0,2,0)*unitcube, white, thick(), nolight);<br />
draw(shift(2,2,0)*unitcube, white, thick(), nolight);<br />
draw(shift(0,3,0)*unitcube, white, thick(), nolight);<br />
draw(shift(0,3,1)*unitcube, white, thick(), nolight);<br />
draw(shift(1,3,0)*unitcube, white, thick(), nolight);<br />
draw(shift(2,3,0)*unitcube, white, thick(), nolight);<br />
draw(shift(2,3,1)*unitcube, white, thick(), nolight);</asy><br />
<br />
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 12</math><br />
<br />
[[2003 AMC 8 Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
<br />
In this addition problem, each letter stands for a different digit. <br />
<br />
<math> \setlength{\tabcolsep}{0.5mm}\begin{array}{cccc}&T & W & O\\ + &T & W & O\\ \hline F& O & U & R\end{array} </math><br />
<br />
If <math>T = 7</math> and the letter <math>O</math> represents an even number, what is the only possible value for <math>W</math>?<br />
<br />
<math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2\qquad \textbf{(D)}\ 3\qquad \textbf{(E)}\ 4</math><br />
<br />
[[2003 AMC 8 Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
<br />
A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?<br />
<br />
<asy><br />
defaultpen(linewidth(0.8));<br />
path p=unitsquare;<br />
draw(p^^shift(0,1)*p^^shift(1,0)*p);<br />
draw(shift(4,0)*p^^shift(5,0)*p^^shift(5,1)*p);<br />
label("FRONT", (1,0), S);<br />
label("SIDE", (5,0), S);</asy><br />
<br />
<math> \textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math><br />
<br />
[[2003 AMC 8 Problems/Problem 15|Solution]]<br />
<br />
==Problem 16==<br />
<br />
Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has 4 seats: 1 driver's seat, 1 front passenger seat, and 2 back passenger seats. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there?<br />
<br />
<math>\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 4 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 24</math><br />
<br />
[[2003 AMC 8 Problems/Problem 16|Solution]]<br />
<br />
==Problem 17==<br />
<br />
The six children listed below are from two families of three siblings each. Each child has blue or brown eyes and black or blond hair. Children from the same family have at least one of these characteristics in common. Which two children are Jim's siblings?<br />
<br />
<cmath> \begin{array}{c|c|c}\text{Child}&\text{Eye Color}&\text{Hair Color}\\ \hline\text{Benjamin}&\text{Blue}&\text{Black}\\ \hline\text{Jim}&\text{Brown}&\text{Blonde}\\ \hline\text{Nadeen}&\text{Brown}&\text{Black}\\ \hline\text{Austin}&\text{Blue}&\text{Blonde}\\ \hline\text{Tevyn}&\text{Blue}&\text{Black}\\ \hline\text{Sue}&\text{Blue}&\text{Blonde}\\ \hline\end{array} </cmath><br />
<br />
<math>\textbf{(A)}\ \text{Nadeen and Austin}\qquad\textbf{(B)}\ \text{Benjamin and Sue}\qquad\textbf{(C)}\ \text{Benjamin and Austin}\qquad\textbf{(D)}\ \text{Nadeen and Tevyn}</math><br />
<br />
<math>\textbf{(E)}\ \text{Austin and Sue} </math><br />
<br />
[[2003 AMC 8 Problems/Problem 17|Solution]]<br />
<br />
==Problem 18==<br />
<br />
Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah's party?<br />
<asy>/* AMC8 2003 #18 Problem */<br />
pair a=(102,256), b=(68,131), c=(162,101), d=(134,150);<br />
pair e=(269,105), f=(359,104), g=(303,12), h=(579,211);<br />
pair i=(534, 342), j=(442,432), k=(374,484), l=(278,501);<br />
pair m=(282,411), n=(147,451), o=(103,437), p=(31,373);<br />
pair q=(419,175), r=(462,209), s=(477,288), t=(443,358);<br />
pair oval=(282,303);<br />
draw(l--m--n--cycle);<br />
draw(p--oval);<br />
draw(o--oval);<br />
draw(b--d--oval);<br />
draw(c--d--e--oval);<br />
draw(e--f--g--h--i--j--oval);<br />
draw(k--oval);<br />
draw(q--oval);<br />
draw(s--oval);<br />
draw(r--s--t--oval);<br />
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h);<br />
dot(i); dot(j); dot(k); dot(l); dot(m); dot(n); dot(o); dot(p);<br />
dot(q); dot(r); dot(s); dot(t);<br />
filldraw(yscale(.5)*Circle((282,606),80),white,black);<br />
label(scale(0.75)*"Sarah", oval);</asy><br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 7</math><br />
<br />
[[2003 AMC 8 Problems/Problem 18|Solution]]<br />
<br />
==Problem 19==<br />
<br />
How many integers between 1000 and 2000 have all three of the numbers 15, 20, and 25 as factors?<br />
<br />
<math>\textbf{(A)}\ 1 \qquad \textbf{(B)}\ 2 \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ 4 \qquad \textbf{(E)}\ 5</math><br />
<br />
[[2003 AMC 8 Problems/Problem 19|Solution]]<br />
<br />
==Problem 20==<br />
<br />
What is the measure of the acute angle formed by the hands of the clock at 4:20 PM?<br />
<br />
<math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 8 \qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}\ 12</math><br />
<br />
[[2003 AMC 8 Problems/Problem 20|Solution]]<br />
<br />
==Problem 21==<br />
<br />
The area of trapezoid <math> ABCD</math> is <math>164\text{ cm}^2</math>. The altitude is 8 cm, <math>AB</math> is 10 cm, and <math>CD</math> is 17 cm. What is <math>BC</math>, in centimeters?<br />
<br />
<asy>/* AMC8 2003 #21 Problem */<br />
size(4inch,2inch);<br />
draw((0,0)--(31,0)--(16,8)--(6,8)--cycle);<br />
draw((11,8)--(11,0), linetype("8 4"));<br />
draw((11,1)--(12,1)--(12,0));<br />
label("$A$", (0,0), SW);<br />
label("$D$", (31,0), SE);<br />
label("$B$", (6,8), NW);<br />
label("$C$", (16,8), NE);<br />
label("10", (3,5), W);<br />
label("8", (11,4), E);<br />
label("17", (22.5,5), E);</asy><br />
<br />
<math> \textbf{(A)}\ 9\qquad\textbf{(B)}\ 10\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 20</math><br />
<br />
[[2003 AMC 8 Problems/Problem 21|Solution]]<br />
<br />
==Problem 22==<br />
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?<br />
<asy>/* AMC8 2003 #22 Problem */<br />
size(3inch, 2inch);<br />
unitsize(1cm);<br />
pen outline = black+linewidth(1);<br />
filldraw((0,0)--(2,0)--(2,2)--(0,2)--cycle, mediumgrey, outline);<br />
filldraw(shift(3,0)*((0,0)--(2,0)--(2,2)--(0,2)--cycle), mediumgrey, outline);<br />
filldraw(Circle((7,1), 1), mediumgrey, black+linewidth(1));<br />
filldraw(Circle((1,1), 1), white, outline);<br />
filldraw(Circle((3.5,.5), .5), white, outline);<br />
filldraw(Circle((4.5,.5), .5), white, outline);<br />
filldraw(Circle((3.5,1.5), .5), white, outline);<br />
filldraw(Circle((4.5,1.5), .5), white, outline);<br />
filldraw((6.3,.3)--(7.7,.3)--(7.7,1.7)--(6.3,1.7)--cycle, white, outline);<br />
label("A", (1, 2), N);<br />
label("B", (4, 2), N);<br />
label("C", (7, 2), N);<br />
draw((0,-.5)--(.5,-.5), BeginArrow);<br />
draw((1.5, -.5)--(2, -.5), EndArrow);<br />
label("2 cm", (1, -.5));<br />
<br />
draw((3,-.5)--(3.5,-.5), BeginArrow);<br />
draw((4.5, -.5)--(5, -.5), EndArrow);<br />
label("2 cm", (4, -.5));<br />
<br />
draw((6,-.5)--(6.5,-.5), BeginArrow);<br />
draw((7.5, -.5)--(8, -.5), EndArrow);<br />
label("2 cm", (7, -.5));<br />
<br />
draw((6,1)--(6,-.5), linetype("4 4"));<br />
draw((8,1)--(8,-.5), linetype("4 4"));</asy><br />
<br />
<math> \textbf{(A)}\ \text{A only}\qquad\textbf{(B)}\ \text{B only}\qquad\textbf{(C)}\ \text{C only}\qquad\textbf{(D)}\ \text{both A and B}\qquad\textbf{(E)}\ \text{all are equal}</math><br />
<br />
[[2003 AMC 8 Problems/Problem 22|Solution]]<br />
<br />
==Problem 23==<br />
In the pattern below, the cat (denoted as a large circle in the figures below) moves clockwise through the four squares and the mouse (denoted as a dot in the figures below) moves counterclockwise through the eight exterior segments of the four squares.<br />
<br />
<center><br />
[[Image:2003amc8prob23a.png|800px]]<br />
</center><br />
<br />
If the pattern is continued, where would the cat and mouse be after the 247th move?<br />
<br />
<center><br />
[[Image:2003amc8prob23b.png|800px]]<br />
</center><br />
<br />
[[2003 AMC 8 Problems/Problem 23|Solution]]<br />
<br />
==Problem 24==<br />
A ship travels from point <math>A</math> to point <math>B</math> along a semicircular path, centered at Island <math>X</math>. Then it travels along a straight path from <math>B</math> to <math>C</math>. Which of these graphs best shows the ship's distance from Island <math>X</math> as it moves along its course?<br />
<br />
<asy>size(150);<br />
pair X=origin, A=(-5,0), B=(5,0), C=(0,5);<br />
draw(Arc(X, 5, 180, 360)^^B--C);<br />
dot(X);<br />
label("$X$", X, NE);<br />
label("$C$", C, N);<br />
label("$B$", B, E);<br />
label("$A$", A, W);<br />
</asy><br />
<br />
<center><br />
[[Image:2003amc8prob24ans.png|800px]]<br />
</center><br />
<br />
[[2003 AMC 8 Problems/Problem 24|Solution]]<br />
<br />
==Problem 25==<br />
In the figure, the area of square <math>WXYZ</math> is <math>25 \text{ cm}^2</math>. The four smaller squares have sides 1 cm long, either parallel to or coinciding with the sides of the large square. In <math>\triangle ABC</math>, <math>AB = AC</math>, and when <math>\triangle ABC</math> is folded over side <math>\overline{BC}</math>, point <math>A</math> coincides with <math>O</math>, the center of square <math>WXYZ</math>. What is the area of <math>\triangle ABC</math>, in square centimeters?<br />
<br />
<asy><br />
defaultpen(fontsize(8));<br />
size(225);<br />
pair Z=origin, W=(0,10), X=(10,10), Y=(10,0), O=(5,5), B=(-4,8), C=(-4,2), A=(-13,5);<br />
draw((-4,0)--Y--X--(-4,10)--cycle);<br />
draw((0,-2)--(0,12)--(-2,12)--(-2,8)--B--A--C--(-2,2)--(-2,-2)--cycle);<br />
dot(O);<br />
label("$A$", A, NW);<br />
label("$O$", O, NE);<br />
label("$B$", B, SW);<br />
label("$C$", C, NW);<br />
label("$W$",W , NE);<br />
label("$X$", X, N);<br />
label("$Y$", Y, S);<br />
label("$Z$", Z, SE);<br />
</asy><br />
<br />
<math> \textbf{(A)}\ \frac{15}4\qquad\textbf{(B)}\ \frac{21}4\qquad\textbf{(C)}\ \frac{27}4\qquad\textbf{(D)}\ \frac{21}2\qquad\textbf{(E)}\ \frac{27}2</math><br />
<br />
[[2003 AMC 8 Problems/Problem 25|Solution]]<br />
<br />
==See Also==<br />
{{AMC8 box|year=2003|before=[[2002 AMC 8 Problems|2002 AMC 8]]|after=[[2004 AMC 8 Problems|2004 AMC 8]]}}<br />
* [[AMC 8]]<br />
* [[AMC 8 Problems and Solutions]]<br />
* [[Mathematics competition resources]]<br />
<br />
<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2003_AMC_8_Problems/Problem_22&diff=717562003 AMC 8 Problems/Problem 222015-08-24T13:17:14Z<p>Bluecarneal: /* Solution */</p>
<hr />
<div>==Problem==<br />
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?<br />
<asy>/* AMC8 2003 #22 Problem */<br />
size(3inch, 2inch);<br />
unitsize(1cm);<br />
pen outline = black+linewidth(1);<br />
filldraw((0,0)--(2,0)--(2,2)--(0,2)--cycle, mediumgrey, outline);<br />
filldraw(shift(3,0)*((0,0)--(2,0)--(2,2)--(0,2)--cycle), mediumgrey, outline);<br />
filldraw(Circle((7,1), 1), mediumgrey, black+linewidth(1));<br />
filldraw(Circle((1,1), 1), white, outline);<br />
filldraw(Circle((3.5,.5), .5), white, outline);<br />
filldraw(Circle((4.5,.5), .5), white, outline);<br />
filldraw(Circle((3.5,1.5), .5), white, outline);<br />
filldraw(Circle((4.5,1.5), .5), white, outline);<br />
filldraw((6.3,.3)--(7.7,.3)--(7.7,1.7)--(6.3,1.7)--cycle, white, outline);<br />
label("A", (1, 2), N);<br />
label("B", (4, 2), N);<br />
label("C", (7, 2), N);<br />
draw((0,-.5)--(.5,-.5), BeginArrow);<br />
draw((1.5, -.5)--(2, -.5), EndArrow);<br />
label("2 cm", (1, -.5));<br />
<br />
draw((3,-.5)--(3.5,-.5), BeginArrow);<br />
draw((4.5, -.5)--(5, -.5), EndArrow);<br />
label("2 cm", (4, -.5));<br />
<br />
draw((6,-.5)--(6.5,-.5), BeginArrow);<br />
draw((7.5, -.5)--(8, -.5), EndArrow);<br />
label("2 cm", (7, -.5));<br />
<br />
draw((6,1)--(6,-.5), linetype("4 4"));<br />
draw((8,1)--(8,-.5), linetype("4 4"));</asy><br />
<br />
<math> \textbf{(A)}\ \text{A only}\qquad\textbf{(B)}\ \text{B only}\qquad\textbf{(C)}\ \text{C only}\qquad\textbf{(D)}\ \text{both A and B}\qquad\textbf{(E)}\ \text{all are equal}</math><br />
<br />
<br />
==Solution==<br />
<br />
First we have to find the area of the shaded region in each of the figures. In figure <math>\textbf{A}</math> the area of the shaded region is the area of the circle subtracted from the area of the square. That is <math>2^2-1^2 \pi=4-\pi</math>. In figure <math>\textbf{B}</math> the area of the shaded region is the sum of the areas of the 4 circles subtracted from the area of the square. That is <math>2^2-4((\frac{1}{2})^2 \pi)=4-4(\frac{\pi}{4})=4-\pi</math>. In figure <math>\textbf{C}</math> the area of the shaded region is the area of the square subtracted from the area of the circle. The diameter of the circle and the diagonal of the square are equal to 2. We can easily find the area of the square using the area formula <math>\frac{d_1 d_2}{2}</math>. So the area of the shaded region is <math>1^2 \pi-\frac{2\cdot{2}}{2}=\pi-2</math>. Clearly the largest area that we found among the three shaded regions is <math>\pi -</math>2. area so the answer is <math>\boxed{C}</math><br />
<br />
==See Also==<br />
{{AMC8 box|year=2003|num-b=21|num-a=23}}<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2004_AMC_8_Problems&diff=716642004 AMC 8 Problems2015-08-17T15:11:55Z<p>Bluecarneal: /* Problem 14 */</p>
<hr />
<div>==Problem 1==<br />
<br />
On a map, a <math>12</math>-centimeter length represents <math>72</math> kilometers. How many kilometers does a <math>17</math>-centimeter length represent?<br />
<br />
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 102\qquad\textbf{(C)}\ 204\qquad\textbf{(D)}\ 864\qquad\textbf{(E)}\ 1224 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 1|Solution]]<br />
<br />
==Problem 2==<br />
<br />
How many different four-digit numbers can be formed be rearranging the four digits in <math>2004</math>?<br />
<br />
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 6\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 24\qquad\textbf{(E)}\ 81 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
<br />
Twelve friends met for dinner at Oscar's Overstuffed Oyster House, and each ordered one meal. The portions were so large, there was enough food for <math>18</math> people. If they shared, how many meals should they have ordered to have just enough food for the <math>12</math> of them?<br />
<br />
<math> \textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 18 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 3|Solution]]<br />
<br />
=='''Basketball Tournament'''==<br />
<br />
Ms. Hamiltonâ€™s eighth-grade class wants to participate in the annual three-person-team basketball tournament.<br />
<br />
==Problem 4==<br />
<br />
Lance, Sally, Joy, and Fred are chosen for the team. In how many ways can the three starters be chosen?<br />
<br />
<math> \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 10 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
<br />
The losing team of each game is eliminated from the tournament. If sixteen teams compete, how many games will be played to determine the winner?<br />
<br />
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 7\qquad\textbf{(C)}\ 8\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 16 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
<br />
After Sally takes <math>20</math> shots, she has made <math>55\%</math> of her shots. After she takes <math>5</math> more shots, she raises her percentage to <math>56\%</math>. How many of the last <math>5</math> shots did she make?<br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
<br />
An athlete's target heart rate, in beats per minute, is <math>80\%</math> of the theoretical maximum heart rate. The maximum heart rate is found by subtracting the athlete's age, in years, from <math>220</math>. To the nearest whole number, what is the target heart rate of an athlete who is <math>26</math> years old?<br />
<br />
<math> \textbf{(A)}\ 134\qquad\textbf{(B)}\ 155\qquad\textbf{(C)}\ 176\qquad\textbf{(D)}\ 194\qquad\textbf{(E)}\ 243 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 7|Solution]]<br />
<br />
==Problem 8==<br />
<br />
Find the number of two-digit positive integers whose digits total <math>7</math>.<br />
<br />
<math> \textbf{(A)}\ 6 \qquad\textbf{(B)}\ 7 \qquad\textbf{(C)}\ 8 \qquad\textbf{(D)}\ 9 \qquad\textbf{(E)}\ 10 </math><br />
<br />
[[2004 AMC 8 Problems/Problem 8|Solution]]<br />
<br />
==Problem 9==<br />
<br />
The average of the five numbers in a list is <math>54</math>. The average of the first two<br />
numbers is <math>48</math>. What is the average of the last three numbers?<br />
<br />
<math> \textbf{(A)}\ 55\qquad\textbf{(B)}\ 56\qquad\textbf{(C)}\ 57\qquad\textbf{(D)}\ 58\qquad\textbf{(E)}\ 59</math><br />
<br />
[[2004 AMC 8 Problems/Problem 9|Solution]]<br />
<br />
==Problem 10==<br />
<br />
Handy Aaron helped a neighbor <math>1 \frac14</math> hours on Monday, <math>50</math> minutes on Tuesday, from 8:20 to 10:45 on Wednesday morning, and a half-hour on Friday. He is paid <math>\textdollar 3</math> per hour. How much did he earn for the week?<br />
<br />
<math>\textbf{(A)}\ \textdollar 8 \qquad \textbf{(B)}\ \textdollar 9 \qquad \textbf{(C)}\ \textdollar 10 \qquad \textbf{(D)}\ \textdollar 12 \qquad \textbf{(E)}\ \textdollar 15</math><br />
<br />
[[2004 AMC 8 Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
<br />
The numbers <math>-2, 4, 6, 9</math> and <math>12</math> are rearranged according to these rules:<br />
<br />
1. The largest isnâ€™t first, but it is in one of the first three places. <br />
2. The smallest isnâ€™t last, but it is in one of the last three places. <br />
3. The median isnâ€™t first or last.<br />
<br />
What is the average of the first and last numbers?<br />
<br />
<math>\textbf{(A)}\ 3.5 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6.5 \qquad \textbf{(D)}\ 7.5 \qquad \textbf{(E)}\ 8</math><br />
<br />
[[2004 AMC 8 Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
<br />
Niki usually leaves her cell phone on. If her cell phone is on but<br />
she is not actually using it, the battery will last for <math>24</math> hours. If<br />
she is using it constantly, the battery will last for only <math>3</math> hours.<br />
Since the last recharge, her phone has been on <math>9</math> hours, and during<br />
that time she has used it for <math>60</math> minutes. If she doesnâ€™t talk any<br />
more but leaves the phone on, how many more hours will the battery last?<br />
<br />
<math>\textbf{(A)}\ 7 \qquad \textbf{(B)}\ 8 \qquad \textbf{(C)}\ 11 \qquad \textbf{(D)}\ 14 \qquad \textbf{(E)}\ 15</math><br />
<br />
[[2004 AMC 8 Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
Amy, Bill and Celine are friends with different ages. Exactly one of the following statements is true.<br />
I. Bill is the oldest.<br />
II. Amy is not the oldest.<br />
III. Celine is not the youngest.<br />
Rank the friends from the oldest to the youngest.<br />
<br />
<math>\textbf{(A)}\ \text{Bill, Amy, Celine}\qquad \textbf{(B)}\ \text{Amy, Bill, Celine}\qquad \textbf{(C)}\ \text{Celine, Amy, Bill}\\<br />
\textbf{(D)}\ \text{Celine, Bill, Amy} \qquad \textbf{(E)}\ \text{Amy, Celine, Bill}</math><br />
<br />
[[2004 AMC 8 Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
What is the area enclosed by the geoboard quadrilateral below?<br />
<br />
<asy><br />
unitsize(3mm);<br />
defaultpen(linewidth(.8pt));<br />
dotfactor=2;<br />
<br />
for(int a=0; a<=10; ++a)<br />
for(int b=0; b<=10; ++b)<br />
{<br />
dot((a,b));<br />
};<br />
<br />
draw((4,0)--(0,5)--(3,4)--(10,10)--cycle);<br />
</asy><br />
<div style="color: green; background-color: yellow;"></div><br />
<math>\textbf{(A)}\ 15\qquad \textbf{(B)}\ 18\frac{1}{2} \qquad \textbf{(C)}\ 22\frac{1}{2} \qquad \textbf{(D)}\ 27 \qquad \textbf{(E)}\ 41</math><br />
<br />
[[2004 AMC 8 Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
Thirteen black and six white hexagonal tiles were used to create the figure below. If a new figures is created by attaching a border of white tiles with the same size and shape as the others, what will be the difference between the total number of white tiles and the total number of black tiles in the new figure?<br />
<br />
<center><br />
[[Image:AMC8200415.gif]]<br />
</center><br />
<br />
<math>\textbf{(A)}\ 5\qquad \textbf{(B)}\ 7\qquad \textbf{(C)}\ 11\qquad \textbf{(D)}\ 12 \qquad \textbf{(E)}\ 18</math><br />
<br />
[[2004 AMC 8 Problems/Problem 15|Solution]]<br />
<br />
==Problem 16==<br />
Two <math>600</math> mL pitchers contain orange juice. One pitcher is <math>1/3</math> full and the other pitcher is <math>2/5</math> full. Water is added to fill each pitcher completely, then both pitchers are poured into one large container. What fraction of the mixture in the large container is orange juice?<br />
<br />
<math>\textbf{(A)}\ \frac18 \qquad \textbf{(B)}\ \frac{3}{16} \qquad \textbf{(C)}\ \frac{11}{30} \qquad \textbf{(D)}\ \frac{11}{19}\qquad \textbf{(E)}\ \frac{11}{15}</math><br />
<br />
[[2004 AMC 8 Problems/Problem 16|Solution]]<br />
<br />
==Problem 17==<br />
Three friends have a total of <math>6</math> identical pencils, and each one has at least one pencil. In how many ways can this happen?<br />
<br />
<math>\textbf{(A)}\ 1\qquad \textbf{(B)}\ 3\qquad \textbf{(C)}\ 6\qquad \textbf{(D)}\ 10 \qquad \textbf{(E)}\ 12</math><br />
<br />
[[2004 AMC 8 Problems/Problem 17|Solution]]<br />
<br />
==Problem 18==<br />
Five friends compete in a dart-throwing contest. Each one has two darts to throw at the same circular target, and each individual's score is the sum of the scores in the target regions that are hit. The scores for the target regions are the whole numbers <math>1</math> through <math>10</math>. Each throw hits the target in a region with a different value. The scores are: Alice <math>16</math> points, Ben <math>4</math> points, Cindy <math>7</math> points, Dave <math>11</math> points, and Ellen <math>17</math> points. Who hits the region worth <math>6</math> points?<br />
<br />
<math>\textbf{(A)}\ \text{Alice}\qquad \textbf{(B)}\ \text{Ben}\qquad \textbf{(C)}\ \text{Cindy}\qquad \textbf{(D)}\ \text{Dave} \qquad \textbf{(E)}\ \text{Ellen}</math><br />
<br />
[[2004 AMC 8 Problems/Problem 18|Solution]]<br />
<br />
==Problem 19==<br />
A whole number larger than <math>2</math> leaves a remainder of <math>2</math> when divided by each of the numbers <math>3, 4, 5,</math> and <math>6</math>. The smallest such number lies between which two numbers?<br />
<br />
<math>\textbf{(A)}\ 40\ \text{and}\ 49 \qquad \textbf{(B)}\ 60 \text{ and } 79 \qquad \textbf{(C)}\ 100\ \text{and}\ 129 \qquad \textbf{(D)}\ 210\ \text{and}\ 249\qquad \textbf{(E)}\ 320\ \text{and}\ 369</math><br />
<br />
[[2004 AMC 8 Problems/Problem 19|Solution]]<br />
<br />
==Problem 20==<br />
Two-thirds of the people in a room are seated in three-fourths of the chairs. The rest of the people are standing. If there are <math>6</math> empty chairs, how many people are in the room?<br />
<br />
<math>\textbf{(A)}\ 12\qquad \textbf{(B)}\ 18\qquad \textbf{(C)}\ 24\qquad \textbf{(D)}\ 27\qquad \textbf{(E)}\ 36</math><br />
<br />
[[2004 AMC 8 Problems/Problem 20|Solution]]<br />
<br />
==Problem 21==<br />
Spinners <math>A</math> and <math>B</math> are spun. On each spinner, the arrow is equally likely to land on each number. What is the probability that the product of the two spinners' numbers is even?<br />
<br />
<asy><br />
pair A=(0,0); pair B=(3,0);<br />
draw(Circle(A,1)); draw(Circle(B,1));<br />
<br />
draw((-1,0)--(1,0)); draw((0,1)--(0,-1));<br />
draw((3,0)--(3,1)); draw((3+sqrt(3)/2,-.5)--(3,0)); draw((3,0)--(3-sqrt(3)/2,-.5)); <br />
<br />
label("$A$",(-1,1));<br />
label("$B$",(2,1));<br />
<br />
label("$1$",(-.4,.4)); label("$2$",(.4,.4)); label("$3$",(.4,-.4)); label("$4$",(-.4,-.4));<br />
label("$1$",(2.6,.4)); label("$2$",(3.4,.4)); label("$3$",(3,-.5));<br />
<br />
</asy><br />
<br />
<math>\textbf{(A)}\ \frac14\qquad \textbf{(B)}\ \frac13\qquad \textbf{(C)}\ \frac12\qquad \textbf{(D)}\ \frac23\qquad \textbf{(E)}\ \frac34</math><br />
<br />
[[2004 AMC 8 Problems/Problem 21|Solution]]<br />
<br />
==Problem 22==<br />
At a party there are only single women and married men with their wives. The probability that a randomly selected woman is single is <math>\frac25</math>. What fraction of the people in the room are married men?<br />
<br />
<math>\textbf{(A)}\ \frac13\qquad \textbf{(B)}\ \frac38\qquad \textbf{(C)}\ \frac25\qquad \textbf{(D)}\ \frac{5}{12}\qquad \textbf{(E)}\ \frac35</math><br />
<br />
[[2004 AMC 8 Problems/Problem 22|Solution]]<br />
<br />
==Problem 23==<br />
Tess runs counterclockwise around rectangular block <math>JKLM</math>. She lives at corner <math>J</math>. Which graph could represent her straight-line distance from home?<br />
<br />
<asy><br />
unitsize(5mm);<br />
pair J=(-3,2); pair K=(-3,-2); pair L=(3,-2); pair M=(3,2); <br />
draw(J--K--L--M--cycle);<br />
label("$J$",J,NW);<br />
label("$K$",K,SW);<br />
label("$L$",L,SE);<br />
label("$M$",M,NE);<br />
</asy><br />
<br />
[[Image:AMC8200423.gif]]<br />
<br />
[[2004 AMC 8 Problems/Problem 23|Solution]]<br />
<br />
==Problem 24==<br />
In the figure, <math>ABCD</math> is a rectangle and <math>EFGH</math> is a parallelogram. Using the measurements given in the figure, what is the length <math>d</math> of the segment that is perpendicular to <math>\overline{HE}</math> and <math>\overline{FG}</math>?<br />
<br />
<asy><br />
unitsize(3mm);<br />
defaultpen(linewidth(.8pt)+fontsize(10pt));<br />
<br />
pair D=(0,0), C=(10,0), B=(10,8), A=(0,8);<br />
pair E=(4,8), F=(10,3), G=(6,0), H=(0,5);<br />
<br />
draw(A--B--C--D--cycle);<br />
draw(E--F--G--H--cycle);<br />
<br />
label("$A$",A,NW);<br />
label("$B$",B,NE);<br />
label("$C$",C,SE);<br />
label("$D$",D,SW);<br />
<br />
label("$E$",E,N);<br />
label("$F$",(10.8,3));<br />
label("$G$",G,S);<br />
label("$H$",H,W);<br />
<br />
label("$4$",A--E,N);<br />
label("$6$",B--E,N);<br />
label("$5$",(10.8,5.5));<br />
label("$3$",(10.8,1.5));<br />
label("$4$",G--C,S);<br />
label("$6$",G--D,S);<br />
label("$5$",D--H,W);<br />
label("$3$",A--H,W);<br />
<br />
draw((3,7.25)--(7.56,1.17));<br />
label("$d$",(3,7.25)--(7.56,1.17), NE);<br />
<br />
</asy><br />
<br />
<math>\textbf{(A)}\ 6.8\qquad \textbf{(B)}\ 7.1\qquad \textbf{(C)}\ 7.6\qquad \textbf{(D)}\ 7.8\qquad \textbf{(E)}\ 8.1</math><br />
<br />
[[2004 AMC 8 Problems/Problem 24|Solution]]<br />
<br />
==Problem 25==<br />
Two <math>4 \times 4</math> squares intersect at right angles, bisecting their intersecting sides, as shown. The circle's diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares?<br />
<br />
<asy><br />
unitsize(6mm);<br />
draw(unitcircle);<br />
filldraw((0,1)--(1,2)--(3,0)--(1,-2)--(0,-1)--(-1,-2)--(-3,0)--(-1,2)--cycle,lightgray,black);<br />
filldraw(unitcircle,white,black);<br />
</asy><br />
<br />
<math>\textbf{(A)}\ 16-4\pi\qquad \textbf{(B)}\ 16-2\pi \qquad \textbf{(C)}\ 28-4\pi \qquad \textbf{(D)}\ 28-2\pi \qquad \textbf{(E)}\ 32-2\pi</math><br />
<br />
[[2004 AMC 8 Problems/Problem 25|Solution]]<br />
<br />
==See Also==<br />
{{AMC8 box|year=2004|before=[[2003 AMC 8 Problems|2003 AMC 8]]|after=[[2005 AMC 8 Problems|2005 AMC 8]]}}<br />
* [[AMC 8]]<br />
* [[AMC 8 Problems and Solutions]]<br />
* [[Mathematics competition resources]]<br />
<br />
<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2005_AMC_8_Problems&diff=713172005 AMC 8 Problems2015-07-25T18:12:56Z<p>Bluecarneal: /* Problem 25 */</p>
<hr />
<div>==Problem 1==<br />
Connie multiplies a number by 2 and gets 60 as her answer. However, she should<br />
have divided the number by 2 to get the correct answer. What is the correct<br />
answer?<br />
<br />
<math> \textbf{(A)}\ 7.5\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 240 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 1|Solution]]<br />
<br />
==Problem 2==<br />
Karl bought five folders from Pay-A-Lot at a cost of <math> \textdollar 2.50 </math> each.<br />
Pay-A-Lot had a 20%-off sale the following day. How much could<br />
Karl have saved on the purchase by waiting a day?<br />
<br />
<math> \textbf{(A)}\ \textdollar 1.00 \qquad\textbf{(B)}\ \textdollar 2.00 \qquad\textbf{(C)}\ \textdollar 2.50\qquad\textbf{(D)}\ \textdollar 2.75 \qquad\textbf{(E)}\ \textdollar 5.00 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal <math> \overline{BD}</math> of square <math> ABCD</math>?<br />
<asy>defaultpen(linewidth(1));<br />
for ( int x = 0; x &lt; 5; ++x )<br />
{<br />
draw((0,x)--(4,x));<br />
draw((x,0)--(x,4));<br />
}<br />
<br />
fill((1,0)--(2,0)--(2,1)--(1,1)--cycle);<br />
fill((0,3)--(1,3)--(1,4)--(0,4)--cycle);<br />
fill((2,3)--(4,3)--(4,4)--(2,4)--cycle);<br />
fill((3,1)--(4,1)--(4,2)--(3,2)--cycle);<br />
label("$A$", (0, 4), NW);<br />
label("$B$", (4, 4), NE);<br />
label("$C$", (4, 0), SE);<br />
label("$D$", (0, 0), SW);</asy><br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 3|Solution]]<br />
<br />
==Problem 4==<br />
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?<br />
<br />
<math> \textbf{(A)}\ 24\qquad\textbf{(B)}\ 25\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 64 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?<br />
<br />
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 15 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
Suppose <math>d</math> is a digit. For how many values of <math>d</math> is <math>2.00d5 > 2.005</math>?<br />
<br />
<math> \textbf{(A)}\ 0\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 10 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
Bill walks <math>\tfrac12</math> mile south, then <math>\tfrac34</math> mile east, and finally <math>\tfrac12</math> mile south. How many miles is he, in a direct line, from his starting point?<br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 1\tfrac14\qquad\textbf{(C)}\ 1\tfrac12\qquad\textbf{(D)}\ 1\tfrac34\qquad\textbf{(E)}\ 2 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 7|Solution]]<br />
<br />
==Problem 8==<br />
Suppose m and n are positive odd integers. Which of the following must also be an odd integer?<br />
<br />
<math> \textbf{(A)}\ m+3n\qquad\textbf{(B)}\ 3m-n\qquad\textbf{(C)}\ 3m^2 + 3n^2\qquad\textbf{(D)}\ (nm + 3)^2\qquad\textbf{(E)}\ 3mn </math><br />
<br />
[[2005 AMC 8 Problems/Problem 8|Solution]]<br />
<br />
==Problem 9==<br />
In quadrilateral <math> ABCD</math>, sides <math> \overline{AB}</math> and <math> \overline{BC}</math> both have length 10, sides <math> \overline{CD}</math> and <math> \overline{DA}</math> both have length 17, and the measure of angle <math> ADC</math> is <math> 60^\circ</math>. What is the length of diagonal <math> \overline{AC}</math>?<br />
<asy>draw((0,0)--(17,0));<br />
draw(rotate(301, (17,0))*(0,0)--(17,0));<br />
picture p;<br />
draw(p, (0,0)--(0,10));<br />
draw(p, rotate(115, (0,10))*(0,0)--(0,10));<br />
add(rotate(3)*p);<br />
<br />
draw((0,0)--(8.25,14.5), linetype("8 8"));<br />
<br />
label("$A$", (8.25, 14.5), N);<br />
label("$B$", (-0.25, 10), W);<br />
label("$C$", (0,0), SW);<br />
label("$D$", (17, 0), E);</asy><br />
<br />
<math> \textbf{(A)}\ 13.5\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 15.5\qquad\textbf{(D)}\ 17\qquad\textbf{(E)}\ 18.5 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 9|Solution]]<br />
<br />
==Problem 10==<br />
Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school?<br />
<br />
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 7.3\qquad\textbf{(C)}\ 7.7\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 8.3 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
The sales tax rate in Bergville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its &#36;90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up &#36;90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up &#36;90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total?<br />
<br />
<math> \textbf{(A)}\ - \textdollar1.06\qquad\textbf{(B)}\ - \textdollar 0.53\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ \textdollar 0.53\qquad\textbf{(E)}\ \textdollar 1.06 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
Big Al the ape ate 100 delicious yellow bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many delicious bananas did Big Al eat on May 5?<br />
<br />
<math> \textbf{(A)}\ 20\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 32\qquad\textbf{(E)}\ 34 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
The area of polygon <math> ABCDEF</math> is 52 with <math> AB=8</math>, <math> BC=9</math> and <math> FA=5</math>. What is <math> DE+EF</math>?<br />
<asy>pair a=(0,9), b=(8,9), c=(8,0), d=(4,0), e=(4,4), f=(0,4);<br />
draw(a--b--c--d--e--f--cycle);<br />
draw(shift(0,-.25)*a--shift(.25,-.25)*a--shift(.25,0)*a);<br />
draw(shift(-.25,0)*b--shift(-.25,-.25)*b--shift(0,-.25)*b);<br />
draw(shift(-.25,0)*c--shift(-.25,.25)*c--shift(0,.25)*c);<br />
draw(shift(.25,0)*d--shift(.25,.25)*d--shift(0,.25)*d);<br />
draw(shift(.25,0)*f--shift(.25,.25)*f--shift(0,.25)*f);<br />
label("$A$", a, NW);<br />
label("$B$", b, NE);<br />
label("$C$", c, SE);<br />
label("$D$", d, SW);<br />
label("$E$", e, SW);<br />
label("$F$", f, SW);<br />
label("5", (0,6.5), W);<br />
label("8", (4,9), N);<br />
label("9", (8, 4.5), E);</asy><br />
<br />
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
The Little Twelve Basketball League has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many games are scheduled?<br />
<br />
<math> \textbf{(A)}\ 80\qquad\textbf{(B)}\ 96\qquad\textbf{(C)}\ 100\qquad\textbf{(D)}\ 108\qquad\textbf{(E)}\ 192 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
How many different isosceles triangles have integer side lengths and perimeter 23?<br />
<br />
<math> \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 11</math><br />
<br />
[[2005 AMC 8 Problems/Problem 15|Solution]]<br />
<br />
==Problem 16==<br />
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?<br />
<br />
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 13\qquad\textbf{(E)}\ 15 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 16|Solution]]<br />
<br />
==Problem 17==<br />
The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?<br />
<asy><br />
for ( int i = 1; i <= 7; ++i )<br />
{<br />
draw((i,0)--(i,6));<br />
}<br />
<br />
for ( int i = 1; i <= 5; ++i )<br />
{<br />
draw((0,i)--(8,i));<br />
}<br />
draw((-0.5,0)--(8,0), linewidth(1));<br />
draw((0,-0.5)--(0,6), linewidth(1));<br />
label("$O$", (0,0), SW);<br />
label(scale(.85)*rotate(90)*"distance", (0, 3), W);<br />
label(scale(.85)*"time", (4, 0), S);<br />
dot((1.25, 4.5));<br />
label(scale(.85)*"Evelyn", (1.25, 4.8), N);<br />
dot((2.5, 2.2));<br />
label(scale(.85)*"Briana", (2.5, 2.2), S);<br />
dot((4.25,5.2));<br />
label(scale(.85)*"Carla", (4.25, 5.2), SE);<br />
dot((5.6, 2.8));<br />
label(scale(.85)*"Debra", (5.6, 2.8), N);<br />
dot((6.8, 1.4));<br />
label(scale(.85)*"Angela", (6.8, 1.4), E);<br />
</asy><br />
<br />
<math> \textbf{(A)}\ \text{Angela}\qquad\textbf{(B)}\ \text{Briana}\qquad\textbf{(C)}\ \text{Carla}\qquad\textbf{(D)}\ \text{Debra}\qquad\textbf{(E)}\ \text{Evelyn} </math><br />
<br />
[[2005 AMC 8 Problems/Problem 17|Solution]]<br />
<br />
==Problem 18==<br />
How many three-digit numbers are divisible by 13?<br />
<br />
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 67\qquad\textbf{(C)}\ 69\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 77</math><br />
<br />
[[2005 AMC 8 Problems/Problem 18|Solution]]<br />
<br />
==Problem 19==<br />
What is the perimeter of trapezoid <math> ABCD</math>?<br />
<br />
<asy>size(3inch, 1.5inch);<br />
pair a=(0,0), b=(18,24), c=(68,24), d=(75,0), f=(68,0), e=(18,0);<br />
draw(a--b--c--d--cycle);<br />
draw(b--e);<br />
draw(shift(0,2)*e--shift(2,2)*e--shift(2,0)*e);<br />
label("30", (9,12), W);<br />
label("50", (43,24), N);<br />
label("25", (71.5, 12), E);<br />
label("24", (18, 12), E);<br />
label("$A$", a, SW);<br />
label("$B$", b, N);<br />
label("$C$", c, N);<br />
label("$D$", d, SE);<br />
label("$E$", e, S);</asy><br />
<br />
<math> \textbf{(A)}\ 180\qquad\textbf{(B)}\ 188\qquad\textbf{(C)}\ 196\qquad\textbf{(D)}\ 200\qquad\textbf{(E)}\ 204 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 19|Solution]]<br />
<br />
==Problem 20==<br />
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise.<br />
In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?<br />
<br />
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 20|Solution]]<br />
<br />
==Problem 21==<br />
How many distinct triangles can be drawn using three of the dots below as vertices?<br />
<br />
<asy>dot(origin^^(1,0)^^(2,0)^^(0,1)^^(1,1)^^(2,1));</asy><br />
<br />
<math> \textbf{(A)}\ 9\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 18\qquad\textbf{(D)}\ 20\qquad\textbf{(E)}\ 24 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 21|Solution]]<br />
<br />
==Problem 22==<br />
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.<br />
<br />
<math> \textbf{(A)}\ \text{SML}\qquad\textbf{(B)}\ \text{LMS}\qquad\textbf{(C)}\ \text{MSL}\qquad\textbf{(D)}\ \text{LSM}\qquad\textbf{(E)}\ \text{MLS} </math><br />
<br />
[[2005 AMC 8 Problems/Problem 22|Solution]]<br />
<br />
==Problem 23==<br />
Isosceles right triangle <math> ABC</math> encloses a semicircle of area <math> 2\pi</math>. The circle has its center <math> O</math> on hypotenuse <math> \overline{AB}</math> and is tangent to sides <math> \overline{AC}</math> and <math> \overline{BC}</math>. What is the area of triangle <math> ABC</math>?<br />
<br />
<asy>pair a=(4,4), b=(0,0), c=(0,4), d=(4,0), o=(2,2);<br />
draw(circle(o, 2));<br />
clip(a--b--c--cycle);<br />
draw(a--b--c--cycle);<br />
dot(o);<br />
label("$C$", c, NW);<br />
label("$A$", a, NE);<br />
label("$B$", b, SW);</asy><br />
<br />
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 3\pi\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 4\pi </math><br />
<br />
[[2005 AMC 8 Problems/Problem 23|Solution]]<br />
<br />
==Problem 24==<br />
A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed "9" and you pressed [+1], it would display "10." If you then pressed [x2], it would display "20." Starting with the display "1," what is the fewest number of keystrokes you would need to reach "200"?<br />
<br />
<math> \textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 12</math><br />
<br />
[[2005 AMC 8 Problems/Problem 24|Solution]]<br />
<br />
==Problem 25==<br />
A square with side length 2 and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?<br />
<br />
<asy>pair a=(4,4), b=(0,0), c=(0,4), d=(4,0), o=(2,2);<br />
draw(a--d--b--c--cycle);<br />
draw(circle(o, 2.25));</asy><br />
<math> \textbf{(A)}\ \frac{2}{\sqrt{\pi}} \qquad \textbf{(B)}\ \frac{1+\sqrt{2}}{2} \qquad \textbf{(C)}\ \frac{3}{2} \qquad \textbf{(D)}\ \sqrt{3} \qquad \textbf{(E)}\ \sqrt{\pi}</math><br />
<br />
[[2005 AMC 8 Problems/Problem 25|Solution]]<br />
<br />
==See Also==<br />
{{AMC8 box|year=2005|before=[[2004 AMC 8 Problems|2004 AMC 8]]|after=[[2006 AMC 8 Problems|2006 AMC 8]]}}<br />
* [[AMC 8]]<br />
* [[AMC 8 Problems and Solutions]]<br />
* [[Mathematics competition resources]]<br />
<br />
<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2005_AMC_8_Problems&diff=713162005 AMC 8 Problems2015-07-25T18:12:32Z<p>Bluecarneal: /* Problem 13 */</p>
<hr />
<div>==Problem 1==<br />
Connie multiplies a number by 2 and gets 60 as her answer. However, she should<br />
have divided the number by 2 to get the correct answer. What is the correct<br />
answer?<br />
<br />
<math> \textbf{(A)}\ 7.5\qquad\textbf{(B)}\ 15\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 120\qquad\textbf{(E)}\ 240 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 1|Solution]]<br />
<br />
==Problem 2==<br />
Karl bought five folders from Pay-A-Lot at a cost of <math> \textdollar 2.50 </math> each.<br />
Pay-A-Lot had a 20%-off sale the following day. How much could<br />
Karl have saved on the purchase by waiting a day?<br />
<br />
<math> \textbf{(A)}\ \textdollar 1.00 \qquad\textbf{(B)}\ \textdollar 2.00 \qquad\textbf{(C)}\ \textdollar 2.50\qquad\textbf{(D)}\ \textdollar 2.75 \qquad\textbf{(E)}\ \textdollar 5.00 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 2|Solution]]<br />
<br />
==Problem 3==<br />
What is the minimum number of small squares that must be colored black so that a line of symmetry lies on the diagonal <math> \overline{BD}</math> of square <math> ABCD</math>?<br />
<asy>defaultpen(linewidth(1));<br />
for ( int x = 0; x &lt; 5; ++x )<br />
{<br />
draw((0,x)--(4,x));<br />
draw((x,0)--(x,4));<br />
}<br />
<br />
fill((1,0)--(2,0)--(2,1)--(1,1)--cycle);<br />
fill((0,3)--(1,3)--(1,4)--(0,4)--cycle);<br />
fill((2,3)--(4,3)--(4,4)--(2,4)--cycle);<br />
fill((3,1)--(4,1)--(4,2)--(3,2)--cycle);<br />
label("$A$", (0, 4), NW);<br />
label("$B$", (4, 4), NE);<br />
label("$C$", (4, 0), SE);<br />
label("$D$", (0, 0), SW);</asy><br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 3|Solution]]<br />
<br />
==Problem 4==<br />
A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?<br />
<br />
<math> \textbf{(A)}\ 24\qquad\textbf{(B)}\ 25\qquad\textbf{(C)}\ 36\qquad\textbf{(D)}\ 48\qquad\textbf{(E)}\ 64 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 4|Solution]]<br />
<br />
==Problem 5==<br />
Soda is sold in packs of 6, 12 and 24 cans. What is the minimum number of packs needed to buy exactly 90 cans of soda?<br />
<br />
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 15 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 5|Solution]]<br />
<br />
==Problem 6==<br />
Suppose <math>d</math> is a digit. For how many values of <math>d</math> is <math>2.00d5 > 2.005</math>?<br />
<br />
<math> \textbf{(A)}\ 0\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 10 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 6|Solution]]<br />
<br />
==Problem 7==<br />
Bill walks <math>\tfrac12</math> mile south, then <math>\tfrac34</math> mile east, and finally <math>\tfrac12</math> mile south. How many miles is he, in a direct line, from his starting point?<br />
<br />
<math> \textbf{(A)}\ 1\qquad\textbf{(B)}\ 1\tfrac14\qquad\textbf{(C)}\ 1\tfrac12\qquad\textbf{(D)}\ 1\tfrac34\qquad\textbf{(E)}\ 2 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 7|Solution]]<br />
<br />
==Problem 8==<br />
Suppose m and n are positive odd integers. Which of the following must also be an odd integer?<br />
<br />
<math> \textbf{(A)}\ m+3n\qquad\textbf{(B)}\ 3m-n\qquad\textbf{(C)}\ 3m^2 + 3n^2\qquad\textbf{(D)}\ (nm + 3)^2\qquad\textbf{(E)}\ 3mn </math><br />
<br />
[[2005 AMC 8 Problems/Problem 8|Solution]]<br />
<br />
==Problem 9==<br />
In quadrilateral <math> ABCD</math>, sides <math> \overline{AB}</math> and <math> \overline{BC}</math> both have length 10, sides <math> \overline{CD}</math> and <math> \overline{DA}</math> both have length 17, and the measure of angle <math> ADC</math> is <math> 60^\circ</math>. What is the length of diagonal <math> \overline{AC}</math>?<br />
<asy>draw((0,0)--(17,0));<br />
draw(rotate(301, (17,0))*(0,0)--(17,0));<br />
picture p;<br />
draw(p, (0,0)--(0,10));<br />
draw(p, rotate(115, (0,10))*(0,0)--(0,10));<br />
add(rotate(3)*p);<br />
<br />
draw((0,0)--(8.25,14.5), linetype("8 8"));<br />
<br />
label("$A$", (8.25, 14.5), N);<br />
label("$B$", (-0.25, 10), W);<br />
label("$C$", (0,0), SW);<br />
label("$D$", (17, 0), E);</asy><br />
<br />
<math> \textbf{(A)}\ 13.5\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 15.5\qquad\textbf{(D)}\ 17\qquad\textbf{(E)}\ 18.5 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 9|Solution]]<br />
<br />
==Problem 10==<br />
Joe had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Joe took 6 minutes to walk half way to school. How many minutes did it take Joe to get from home to school?<br />
<br />
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 7.3\qquad\textbf{(C)}\ 7.7\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 8.3 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 10|Solution]]<br />
<br />
==Problem 11==<br />
The sales tax rate in Bergville is 6%. During a sale at the Bergville Coat Closet, the price of a coat is discounted 20% from its &#36;90.00 price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up &#36;90.00 and adds 6% sales tax, then subtracts 20% from this total. Jill rings up &#36;90.00, subtracts 20% of the price, then adds 6% of the discounted price for sales tax. What is Jack's total minus Jill's total?<br />
<br />
<math> \textbf{(A)}\ - \textdollar1.06\qquad\textbf{(B)}\ - \textdollar 0.53\qquad\textbf{(C)}\ 0\qquad\textbf{(D)}\ \textdollar 0.53\qquad\textbf{(E)}\ \textdollar 1.06 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 11|Solution]]<br />
<br />
==Problem 12==<br />
Big Al the ape ate 100 delicious yellow bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many delicious bananas did Big Al eat on May 5?<br />
<br />
<math> \textbf{(A)}\ 20\qquad\textbf{(B)}\ 22\qquad\textbf{(C)}\ 30\qquad\textbf{(D)}\ 32\qquad\textbf{(E)}\ 34 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 12|Solution]]<br />
<br />
==Problem 13==<br />
The area of polygon <math> ABCDEF</math> is 52 with <math> AB=8</math>, <math> BC=9</math> and <math> FA=5</math>. What is <math> DE+EF</math>?<br />
<asy>pair a=(0,9), b=(8,9), c=(8,0), d=(4,0), e=(4,4), f=(0,4);<br />
draw(a--b--c--d--e--f--cycle);<br />
draw(shift(0,-.25)*a--shift(.25,-.25)*a--shift(.25,0)*a);<br />
draw(shift(-.25,0)*b--shift(-.25,-.25)*b--shift(0,-.25)*b);<br />
draw(shift(-.25,0)*c--shift(-.25,.25)*c--shift(0,.25)*c);<br />
draw(shift(.25,0)*d--shift(.25,.25)*d--shift(0,.25)*d);<br />
draw(shift(.25,0)*f--shift(.25,.25)*f--shift(0,.25)*f);<br />
label("$A$", a, NW);<br />
label("$B$", b, NE);<br />
label("$C$", c, SE);<br />
label("$D$", d, SW);<br />
label("$E$", e, SW);<br />
label("$F$", f, SW);<br />
label("5", (0,6.5), W);<br />
label("8", (4,9), N);<br />
label("9", (8, 4.5), E);</asy><br />
<br />
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 11 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 13|Solution]]<br />
<br />
==Problem 14==<br />
The Little Twelve Basketball League has two divisions, with six teams in each division. Each team plays each of the other teams in its own division twice and every team in the other division once. How many games are scheduled?<br />
<br />
<math> \textbf{(A)}\ 80\qquad\textbf{(B)}\ 96\qquad\textbf{(C)}\ 100\qquad\textbf{(D)}\ 108\qquad\textbf{(E)}\ 192 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 14|Solution]]<br />
<br />
==Problem 15==<br />
How many different isosceles triangles have integer side lengths and perimeter 23?<br />
<br />
<math> \textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 11</math><br />
<br />
[[2005 AMC 8 Problems/Problem 15|Solution]]<br />
<br />
==Problem 16==<br />
A five-legged Martian has a drawer full of socks, each of which is red, white or blue, and there are at least five socks of each color. The Martian pulls out one sock at a time without looking. How many socks must the Martian remove from the drawer to be certain there will be 5 socks of the same color?<br />
<br />
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 13\qquad\textbf{(E)}\ 15 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 16|Solution]]<br />
<br />
==Problem 17==<br />
The results of a cross-country team's training run are graphed below. Which student has the greatest average speed?<br />
<asy><br />
for ( int i = 1; i <= 7; ++i )<br />
{<br />
draw((i,0)--(i,6));<br />
}<br />
<br />
for ( int i = 1; i <= 5; ++i )<br />
{<br />
draw((0,i)--(8,i));<br />
}<br />
draw((-0.5,0)--(8,0), linewidth(1));<br />
draw((0,-0.5)--(0,6), linewidth(1));<br />
label("$O$", (0,0), SW);<br />
label(scale(.85)*rotate(90)*"distance", (0, 3), W);<br />
label(scale(.85)*"time", (4, 0), S);<br />
dot((1.25, 4.5));<br />
label(scale(.85)*"Evelyn", (1.25, 4.8), N);<br />
dot((2.5, 2.2));<br />
label(scale(.85)*"Briana", (2.5, 2.2), S);<br />
dot((4.25,5.2));<br />
label(scale(.85)*"Carla", (4.25, 5.2), SE);<br />
dot((5.6, 2.8));<br />
label(scale(.85)*"Debra", (5.6, 2.8), N);<br />
dot((6.8, 1.4));<br />
label(scale(.85)*"Angela", (6.8, 1.4), E);<br />
</asy><br />
<br />
<math> \textbf{(A)}\ \text{Angela}\qquad\textbf{(B)}\ \text{Briana}\qquad\textbf{(C)}\ \text{Carla}\qquad\textbf{(D)}\ \text{Debra}\qquad\textbf{(E)}\ \text{Evelyn} </math><br />
<br />
[[2005 AMC 8 Problems/Problem 17|Solution]]<br />
<br />
==Problem 18==<br />
How many three-digit numbers are divisible by 13?<br />
<br />
<math> \textbf{(A)}\ 7\qquad\textbf{(B)}\ 67\qquad\textbf{(C)}\ 69\qquad\textbf{(D)}\ 76\qquad\textbf{(E)}\ 77</math><br />
<br />
[[2005 AMC 8 Problems/Problem 18|Solution]]<br />
<br />
==Problem 19==<br />
What is the perimeter of trapezoid <math> ABCD</math>?<br />
<br />
<asy>size(3inch, 1.5inch);<br />
pair a=(0,0), b=(18,24), c=(68,24), d=(75,0), f=(68,0), e=(18,0);<br />
draw(a--b--c--d--cycle);<br />
draw(b--e);<br />
draw(shift(0,2)*e--shift(2,2)*e--shift(2,0)*e);<br />
label("30", (9,12), W);<br />
label("50", (43,24), N);<br />
label("25", (71.5, 12), E);<br />
label("24", (18, 12), E);<br />
label("$A$", a, SW);<br />
label("$B$", b, N);<br />
label("$C$", c, N);<br />
label("$D$", d, SE);<br />
label("$E$", e, S);</asy><br />
<br />
<math> \textbf{(A)}\ 180\qquad\textbf{(B)}\ 188\qquad\textbf{(C)}\ 196\qquad\textbf{(D)}\ 200\qquad\textbf{(E)}\ 204 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 19|Solution]]<br />
<br />
==Problem 20==<br />
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise.<br />
In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?<br />
<br />
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 20|Solution]]<br />
<br />
==Problem 21==<br />
How many distinct triangles can be drawn using three of the dots below as vertices?<br />
<br />
<asy>dot(origin^^(1,0)^^(2,0)^^(0,1)^^(1,1)^^(2,1));</asy><br />
<br />
<math> \textbf{(A)}\ 9\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 18\qquad\textbf{(D)}\ 20\qquad\textbf{(E)}\ 24 </math><br />
<br />
[[2005 AMC 8 Problems/Problem 21|Solution]]<br />
<br />
==Problem 22==<br />
A company sells detergent in three different sized boxes: small (S), medium (M) and large (L). The medium size costs 50% more than the small size and contains 20% less detergent than the large size. The large size contains twice as much detergent as the small size and costs 30% more than the medium size. Rank the three sizes from best to worst buy.<br />
<br />
<math> \textbf{(A)}\ \text{SML}\qquad\textbf{(B)}\ \text{LMS}\qquad\textbf{(C)}\ \text{MSL}\qquad\textbf{(D)}\ \text{LSM}\qquad\textbf{(E)}\ \text{MLS} </math><br />
<br />
[[2005 AMC 8 Problems/Problem 22|Solution]]<br />
<br />
==Problem 23==<br />
Isosceles right triangle <math> ABC</math> encloses a semicircle of area <math> 2\pi</math>. The circle has its center <math> O</math> on hypotenuse <math> \overline{AB}</math> and is tangent to sides <math> \overline{AC}</math> and <math> \overline{BC}</math>. What is the area of triangle <math> ABC</math>?<br />
<br />
<asy>pair a=(4,4), b=(0,0), c=(0,4), d=(4,0), o=(2,2);<br />
draw(circle(o, 2));<br />
clip(a--b--c--cycle);<br />
draw(a--b--c--cycle);<br />
dot(o);<br />
label("$C$", c, NW);<br />
label("$A$", a, NE);<br />
label("$B$", b, SW);</asy><br />
<br />
<math> \textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 3\pi\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 4\pi </math><br />
<br />
[[2005 AMC 8 Problems/Problem 23|Solution]]<br />
<br />
==Problem 24==<br />
A certain calculator has only two keys [+1] and [x2]. When you press one of the keys, the calculator automatically displays the result. For instance, if the calculator originally displayed "9" and you pressed [+1], it would display "10." If you then pressed [x2], it would display "20." Starting with the display "1," what is the fewest number of keystrokes you would need to reach "200"?<br />
<br />
<math> \textbf{(A)}\ 8\qquad\textbf{(B)}\ 9\qquad\textbf{(C)}\ 10\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 12</math><br />
<br />
[[2005 AMC 8 Problems/Problem 24|Solution]]<br />
<br />
==Problem 25==<br />
A square with side length 2 and a circle share the same center. The total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. What is the radius of the circle?<br />
<br />
<asy>pair a=(4,4), b=(0,0), c=(0,4), d=(4,0), o=(2,2);<br />
draw(a--d--b--c--cycle);<br />
draw(circle(o, 2.25));</asy><br />
<math> \textbf{(A)}\ \frac{2}{\sqrt{\pi}} \qquad \textbf{(B)}\ \frac{1\plus{}\sqrt{2}}{2} \qquad \textbf{(C)}\ \frac{3}{2} \qquad \textbf{(D)}\ \sqrt{3} \qquad \textbf{(E)}\ \sqrt{\pi}</math><br />
<br />
[[2005 AMC 8 Problems/Problem 25|Solution]]<br />
<br />
==See Also==<br />
{{AMC8 box|year=2005|before=[[2004 AMC 8 Problems|2004 AMC 8]]|after=[[2006 AMC 8 Problems|2006 AMC 8]]}}<br />
* [[AMC 8]]<br />
* [[AMC 8 Problems and Solutions]]<br />
* [[Mathematics competition resources]]<br />
<br />
<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2004_AMC_12A_Problems/Problem_18&diff=713142004 AMC 12A Problems/Problem 182015-07-25T18:10:35Z<p>Bluecarneal: </p>
<hr />
<div>{{duplicate|[[2004 AMC 12A Problems|2004 AMC 12A #18]] and [[2004 AMC 10A Problems/Problem 22|2004 AMC 10A #22]]}}<br />
<br />
==Problem==<br />
[[Square]] <math>ABCD</math> has side length <math>2</math>. A [[semicircle]] with [[diameter]] <math>\overline{AB}</math> is constructed inside the square, and the [[tangent (geometry)|tangent]] to the semicircle from <math>C</math> intersects side <math>\overline{AD}</math> at <math>E</math>. What is the length of <math>\overline{CE}</math>?<br />
<br />
<asy><br />
size(100);<br />
defaultpen(fontsize(10));<br />
pair A=(0,0), B=(2,0), C=(2,2), D=(0,2), E=(0,1/2);<br />
draw(A--B--C--D--cycle);draw(C--E);<br />
draw(Arc((1,0),1,0,180));<br />
label("$A$",A,(-1,-1));<br />
label("$B$",B,( 1,-1));<br />
label("$C$",C,( 1, 1));<br />
label("$D$",D,(-1, 1));<br />
label("$E$",E,(-1, 0));<br />
</asy><br />
<br />
<math> \mathrm{(A) \ } \frac{2+\sqrt{5}}{2} \qquad \mathrm{(B) \ } \sqrt{5} \qquad \mathrm{(C) \ } \sqrt{6} \qquad \mathrm{(D) \ } \frac{5}{2} \qquad \mathrm{(E) \ } 5-\sqrt{5} </math><br />
<br />
__TOC__<br />
== Solution 1 ==<br />
<br />
<asy><br />
size(150);<br />
defaultpen(fontsize(10));<br />
pair A=(0,0), B=(2,0), C=(2,2), D=(0,2), E=(0,1/2), F=E+(C-E)/abs(C-E)/2;<br />
draw(A--B--C--D--cycle);draw(C--E);<br />
draw(Arc((1,0),1,0,180));draw((A+B)/2--F);<br />
label("$A$",A,(-1,-1));<br />
label("$B$",B,( 1,-1));<br />
label("$C$",C,( 1, 1));<br />
label("$D$",D,(-1, 1));<br />
label("$E$",E,(-1, 0));<br />
label("$F$",F,( 0, 1));<br />
label("$x$",(A+E)/2,(-1, 0));<br />
label("$x$",(E+F)/2,( 0, 1));<br />
label("$2$",(F+C)/2,( 0, 1));<br />
label("$2$",(D+C)/2,( 0, 1));<br />
label("$2$",(B+C)/2,( 1, 0));<br />
label("$2-x$",(D+E)/2,(-1, 0));<br />
</asy><br />
Let the point of tangency be <math>F</math>. By the [[Two Tangent Theorem]] <math>BC = FC = 2</math> and <math>AE = EF = x</math>. Thus <math>DE = 2-x</math>. The [[Pythagorean Theorem]] on <math>\triangle CDE</math> yields<br />
<br />
<cmath>\begin{align*}<br />
DE^2 + CD^2 &= CE^2\\<br />
(2-x)^2 + 2^2 &= (2+x)^2\\<br />
x^2 - 4x + 8 &= x^2 + 4x + 4\\<br />
x &= \frac{1}{2}\end{align*}</cmath><br />
<br />
Hence <math>CE = FC + x = \frac{5}{2} \Rightarrow\boxed{\mathrm{(D)}\ \frac{5}{2}}</math>.<br />
<br />
<br />
== Solution 2 ==<br />
<br />
[[Image:2004_AMC12A-18.png]]<br />
<br />
Clearly, <math>EA = EF = BG</math>. Thus, the sides of [[right triangle]] <math>CDE</math> are in arithmetic progression. Thus it is [[similar triangles|similar]] to the triangle <math>3 - 4 - 5</math> and since <math>DC = 2</math>, <math>CE = 5/2</math>.<br />
<br />
== Solution 3 == <br />
[[Image:2004_AMC12A-18.png]]<br />
TBE<br />
<br />
== See also ==<br />
* [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=131334 AoPS topic]<br />
{{AMC12 box|year=2004|ab=A|num-b=17|num-a=19}}<br />
{{AMC10 box|year=2004|ab=A|num-b=21|num-a=23}}<br />
<br />
[[Category:Intermediate Geometry Problems]]<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2015_AIME_II_Problems/Problem_7&diff=712022015 AIME II Problems/Problem 72015-07-17T16:14:49Z<p>Bluecarneal: /* Solution 4 */</p>
<hr />
<div>==Problem==<br />
<br />
Triangle <math>ABC</math> has side lengths <math>AB = 12</math>, <math>BC = 25</math>, and <math>CA = 17</math>. Rectangle <math>PQRS</math> has vertex <math>P</math> on <math>\overline{AB}</math>, vertex <math>Q</math> on <math>\overline{AC}</math>, and vertices <math>R</math> and <math>S</math> on <math>\overline{BC}</math>. In terms of the side length <math>PQ = w</math>, the area of <math>PQRS</math> can be expressed as the quadratic polynomial<br />
<br />
Area(<math>PQRS</math>) = <math>\alpha w - \beta \cdot w^2</math>.<br />
<br />
Then the coefficient <math>\beta = \frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.<br />
<br />
==Solution 1==<br />
<br />
If <math>\omega = 25</math>, the area of rectangle <math>PQRS</math> is <math>0</math>, so<br />
<br />
<cmath>\alpha\omega - \beta\omega^2 = 25\alpha - 625\beta = 0</cmath><br />
<br />
and <math>\alpha = 25\beta</math>. If <math>\omega = \frac{25}{2}</math>, we can reflect <math>APQ</math> over PQ, <math>PBS</math> over <math>PS</math>, and <math>QCR</math> over <math>QR</math> to completely cover rectangle <math>PQRS</math>, so the area of <math>PQRS</math> is half the area of the triangle. Using Heron's formula, since <math>s = \frac{12 + 17 + 25}{2} = 27</math>, <br />
<br />
<cmath> [ABC] = \sqrt{27 \cdot 15 \cdot 10 \cdot 2} = 90</cmath><br />
<br />
so<br />
<br />
<cmath>45 = \alpha\omega - \beta\omega^2 = \frac{625}{2} \beta - \beta\frac{625}{4} = \beta\frac{625}{4}</cmath><br />
<br />
and <br />
<br />
<cmath>\beta = \frac{180}{625} = \frac{36}{125}</cmath><br />
<br />
so the answer is <math>m + n = 36 + 125 = \boxed{161}</math>.<br />
<br />
==Solution 2==<br />
<asy><br />
unitsize(20);<br />
pair A,B,C,E,F,P,Q,R,S;<br />
A=(48/5,36/5);<br />
B=(0,0);<br />
C=(25,0);<br />
E=(48/5,0);<br />
F=(48/5,18/5);<br />
P=(24/5,18/5);<br />
Q=(173/10,18/5);<br />
S=(24/5,0);<br />
R=(173/10,0);<br />
draw(A--B--C--cycle);<br />
draw(P--Q);<br />
draw(Q--R);<br />
draw(R--S);<br />
draw(S--P);<br />
draw(A--E,dashed);<br />
label("$A$",A,N);<br />
label("$B$",B,SW);<br />
label("$C$",C,SE);<br />
label("$E$",E,SE);<br />
label("$F$",F,NE);<br />
label("$P$",P,NW);<br />
label("$Q$",Q,NE);<br />
label("$R$",R,SE);<br />
label("$S$",S,SW);<br />
draw(rightanglemark(B,E,A,12));<br />
dot(E);<br />
dot(F);<br />
</asy><br />
<br />
Similar triangles can also solve the problem.<br />
<br />
First, solve for the area of the triangle. <math>[ABC] = 90</math>. This can be done by Heron's Formula or placing an <math>8-15-17</math> right triangle on <math>BC</math> and solving. (The <math>8</math> side would be collinear with line <math>AB</math>)<br />
<br />
After finding the area, solve for the altitude to <math>BC</math>. Let <math>E</math> be the intersection of the altitude from <math>A</math> and side <math>BC</math>. Then <math>AE = \frac{36}{5}</math>. <br />
Solving for <math>BE</math> using the Pythagorean Formula, we get <math>BE = \frac{48}{5}</math>. We then know that <math>CE = \frac{77}{5}</math>.<br />
<br />
Now consider the rectangle <math>PQRS</math>. Since <math>SR</math> is collinear with <math>BC</math> and parallel to <math>PQ</math>, <math>PQ</math> is parallel to <math>BC</math> meaning <math>\Delta APQ</math> is similar to <math>\Delta ABC</math>. <br />
<br />
Let <math>F</math> be the intersection between <math>AE</math> and <math>PQ</math>. By the similar triangles, we know that <math>\frac{PF}{FQ}=\frac{BE}{EC} = \frac{48}{77}</math>. Since <math>PF+FQ=PQ=\omega</math>. We can solve for <math>PF</math> and <math>FQ</math> in terms of <math>\omega</math>. We get that <math>PF=\frac{48}{125} \omega</math> and <math>FQ=\frac{77}{125} \omega</math>.<br />
<br />
Let's work with <math>PF</math>. We know that <math>PQ</math> is parallel to <math>BC</math> so <math>\Delta APF</math> is similar to <math>\Delta ABE</math>. We can set up the proportion:<br />
<br />
<math>\frac{AF}{PF}=\frac{AE}{BE}=\frac{3}{4}</math>. Solving for <math>AF</math>, <math>AF = \frac{3}{4} PF = \frac{3}{4} \cdot \frac{48}{125} \omega = \frac{36}{125} \omega</math>. <br />
<br />
We can solve for <math>PS</math> then since we know that <math>PS=FE</math> and <math>FE= AE - AF = \frac{36}{5} - \frac{36}{125} \omega</math>.<br />
<br />
Therefore, <math>[PQRS] = PQ \cdot PS = \omega (\frac{36}{5} - \frac{36}{125} \omega) = \frac{36}{5}\omega - \frac{36}{125} \omega^2</math>.<br />
<br />
This means that <math>\beta = \frac{36}{125} \Rightarrow (m,n) = (36,125) \Rightarrow m+n = \boxed{161}</math>.<br />
<br />
==Solution 3==<br />
Heron's Formula gives <math>[ABC] = \sqrt{27 \cdot 15 \cdot 10 \cdot 2} = 90,</math> so the altitude from <math>A</math> to <math>BC</math> has length <math>\dfrac{2[ABC]}{BC} = \dfrac{36}{5}.</math><br />
<br />
Now, draw a parallel to <math>AB</math> from <math>Q</math>, intersecting <math>BC</math> at <math>T</math>. Then <math>BT = w</math> in parallelogram <math>QPBT</math>, and so <math>CT = 25 - w</math>. Clearly, <math>CQT</math> and <math>CAB</math> are similar triangles, and so their altitudes have lengths proportional to their corresponding base sides, and so<br />
<cmath>\frac{QR}{\frac{36}{5}} = \frac{25 - w}{25}.</cmath><br />
Solving gives <math>[PQRS] = \dfrac{36}{5} \cdot \dfrac{25 - w}{25} = \dfrac{36w}{5} - \dfrac{36w^2}{125}</math>, so the answer is <math>36 + 125 = 161</math>.<br />
<br />
<br />
==Solution 4==<br />
Using the diagram from Solution 2 above, label <math>AF</math> to be <math>h</math>. Through Heron's formula, the area of <math>\triangle ABC</math> turns out to be <math>90</math>, so using <math>AE</math> as the height and <math>BC</math> as the base yields <math>AE=\frac{36}{5}</math>. Now, through the use of similarity between <math>\triangle APQ</math> and <math>\triangle ABC</math>, you find <math>\frac{w}{25}=\frac{h}{36/5}</math>. Thus, <math>h=\frac{36w}{125}</math>. To find the height of the rectangle, subtract <math>h</math> from <math>\frac{36}{5}</math> to get <math>\left(\frac{36}{5}-\frac{36w}{125}\right)</math>, and multiply this by the other given side <math>w</math> to get <math>\frac{36w}{5}-\frac{36w^2}{125}</math> for the area of the rectangle. Finally, <math>36+125=\boxed{161}</math>.<br />
<br />
==See also==<br />
{{AIME box|year=2015|n=II|num-b=6|num-a=8}}<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2015_AIME_II_Problems/Problem_7&diff=712012015 AIME II Problems/Problem 72015-07-17T16:13:16Z<p>Bluecarneal: /* Solution 4 */</p>
<hr />
<div>==Problem==<br />
<br />
Triangle <math>ABC</math> has side lengths <math>AB = 12</math>, <math>BC = 25</math>, and <math>CA = 17</math>. Rectangle <math>PQRS</math> has vertex <math>P</math> on <math>\overline{AB}</math>, vertex <math>Q</math> on <math>\overline{AC}</math>, and vertices <math>R</math> and <math>S</math> on <math>\overline{BC}</math>. In terms of the side length <math>PQ = w</math>, the area of <math>PQRS</math> can be expressed as the quadratic polynomial<br />
<br />
Area(<math>PQRS</math>) = <math>\alpha w - \beta \cdot w^2</math>.<br />
<br />
Then the coefficient <math>\beta = \frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.<br />
<br />
==Solution 1==<br />
<br />
If <math>\omega = 25</math>, the area of rectangle <math>PQRS</math> is <math>0</math>, so<br />
<br />
<cmath>\alpha\omega - \beta\omega^2 = 25\alpha - 625\beta = 0</cmath><br />
<br />
and <math>\alpha = 25\beta</math>. If <math>\omega = \frac{25}{2}</math>, we can reflect <math>APQ</math> over PQ, <math>PBS</math> over <math>PS</math>, and <math>QCR</math> over <math>QR</math> to completely cover rectangle <math>PQRS</math>, so the area of <math>PQRS</math> is half the area of the triangle. Using Heron's formula, since <math>s = \frac{12 + 17 + 25}{2} = 27</math>, <br />
<br />
<cmath> [ABC] = \sqrt{27 \cdot 15 \cdot 10 \cdot 2} = 90</cmath><br />
<br />
so<br />
<br />
<cmath>45 = \alpha\omega - \beta\omega^2 = \frac{625}{2} \beta - \beta\frac{625}{4} = \beta\frac{625}{4}</cmath><br />
<br />
and <br />
<br />
<cmath>\beta = \frac{180}{625} = \frac{36}{125}</cmath><br />
<br />
so the answer is <math>m + n = 36 + 125 = \boxed{161}</math>.<br />
<br />
==Solution 2==<br />
<asy><br />
unitsize(20);<br />
pair A,B,C,E,F,P,Q,R,S;<br />
A=(48/5,36/5);<br />
B=(0,0);<br />
C=(25,0);<br />
E=(48/5,0);<br />
F=(48/5,18/5);<br />
P=(24/5,18/5);<br />
Q=(173/10,18/5);<br />
S=(24/5,0);<br />
R=(173/10,0);<br />
draw(A--B--C--cycle);<br />
draw(P--Q);<br />
draw(Q--R);<br />
draw(R--S);<br />
draw(S--P);<br />
draw(A--E,dashed);<br />
label("$A$",A,N);<br />
label("$B$",B,SW);<br />
label("$C$",C,SE);<br />
label("$E$",E,SE);<br />
label("$F$",F,NE);<br />
label("$P$",P,NW);<br />
label("$Q$",Q,NE);<br />
label("$R$",R,SE);<br />
label("$S$",S,SW);<br />
draw(rightanglemark(B,E,A,12));<br />
dot(E);<br />
dot(F);<br />
</asy><br />
<br />
Similar triangles can also solve the problem.<br />
<br />
First, solve for the area of the triangle. <math>[ABC] = 90</math>. This can be done by Heron's Formula or placing an <math>8-15-17</math> right triangle on <math>BC</math> and solving. (The <math>8</math> side would be collinear with line <math>AB</math>)<br />
<br />
After finding the area, solve for the altitude to <math>BC</math>. Let <math>E</math> be the intersection of the altitude from <math>A</math> and side <math>BC</math>. Then <math>AE = \frac{36}{5}</math>. <br />
Solving for <math>BE</math> using the Pythagorean Formula, we get <math>BE = \frac{48}{5}</math>. We then know that <math>CE = \frac{77}{5}</math>.<br />
<br />
Now consider the rectangle <math>PQRS</math>. Since <math>SR</math> is collinear with <math>BC</math> and parallel to <math>PQ</math>, <math>PQ</math> is parallel to <math>BC</math> meaning <math>\Delta APQ</math> is similar to <math>\Delta ABC</math>. <br />
<br />
Let <math>F</math> be the intersection between <math>AE</math> and <math>PQ</math>. By the similar triangles, we know that <math>\frac{PF}{FQ}=\frac{BE}{EC} = \frac{48}{77}</math>. Since <math>PF+FQ=PQ=\omega</math>. We can solve for <math>PF</math> and <math>FQ</math> in terms of <math>\omega</math>. We get that <math>PF=\frac{48}{125} \omega</math> and <math>FQ=\frac{77}{125} \omega</math>.<br />
<br />
Let's work with <math>PF</math>. We know that <math>PQ</math> is parallel to <math>BC</math> so <math>\Delta APF</math> is similar to <math>\Delta ABE</math>. We can set up the proportion:<br />
<br />
<math>\frac{AF}{PF}=\frac{AE}{BE}=\frac{3}{4}</math>. Solving for <math>AF</math>, <math>AF = \frac{3}{4} PF = \frac{3}{4} \cdot \frac{48}{125} \omega = \frac{36}{125} \omega</math>. <br />
<br />
We can solve for <math>PS</math> then since we know that <math>PS=FE</math> and <math>FE= AE - AF = \frac{36}{5} - \frac{36}{125} \omega</math>.<br />
<br />
Therefore, <math>[PQRS] = PQ \cdot PS = \omega (\frac{36}{5} - \frac{36}{125} \omega) = \frac{36}{5}\omega - \frac{36}{125} \omega^2</math>.<br />
<br />
This means that <math>\beta = \frac{36}{125} \Rightarrow (m,n) = (36,125) \Rightarrow m+n = \boxed{161}</math>.<br />
<br />
==Solution 3==<br />
Heron's Formula gives <math>[ABC] = \sqrt{27 \cdot 15 \cdot 10 \cdot 2} = 90,</math> so the altitude from <math>A</math> to <math>BC</math> has length <math>\dfrac{2[ABC]}{BC} = \dfrac{36}{5}.</math><br />
<br />
Now, draw a parallel to <math>AB</math> from <math>Q</math>, intersecting <math>BC</math> at <math>T</math>. Then <math>BT = w</math> in parallelogram <math>QPBT</math>, and so <math>CT = 25 - w</math>. Clearly, <math>CQT</math> and <math>CAB</math> are similar triangles, and so their altitudes have lengths proportional to their corresponding base sides, and so<br />
<cmath>\frac{QR}{\frac{36}{5}} = \frac{25 - w}{25}.</cmath><br />
Solving gives <math>[PQRS] = \dfrac{36}{5} \cdot \dfrac{25 - w}{25} = \dfrac{36w}{5} - \dfrac{36w^2}{125}</math>, so the answer is <math>36 + 125 = 161</math>.<br />
<br />
<br />
==Solution 4==<br />
Using the diagram from solution 2 above, label <math>AF</math> to be <math>h</math>. Through Heron's formula, the area of <math>\triangle ABC</math> turns out to be <math>90</math>, so using <math>AE</math> as the height and <math>BC</math> as the base yields <math>AE=\frac{36}{5}</math>. Now, through the use of similarity between <math>\triangle APQ</math> and <math>\triangle ABC</math>, you find <math>\frac{w}{25}=\frac{h}{36/5}</math>. Thus, <math>h=\frac{36w}{125}</math>. To find the height of the rectangle, subtract <math>h</math> from <math>\frac{36}{5}</math> to get <math>\left(\frac{36}{5}-\frac{36w}{125}\right)</math>, and multiply this by the other given side <math>w</math> to get <math>\frac{36w}{5}-\frac{36w^2}{125}</math> for the area of the rectangle. Finally, <math>36+125=\boxed{161}</math>.<br />
<br />
==See also==<br />
{{AIME box|year=2015|n=II|num-b=6|num-a=8}}<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=2015_AIME_II_Problems/Problem_7&diff=712002015 AIME II Problems/Problem 72015-07-17T16:12:59Z<p>Bluecarneal: /* Solution 4 */</p>
<hr />
<div>==Problem==<br />
<br />
Triangle <math>ABC</math> has side lengths <math>AB = 12</math>, <math>BC = 25</math>, and <math>CA = 17</math>. Rectangle <math>PQRS</math> has vertex <math>P</math> on <math>\overline{AB}</math>, vertex <math>Q</math> on <math>\overline{AC}</math>, and vertices <math>R</math> and <math>S</math> on <math>\overline{BC}</math>. In terms of the side length <math>PQ = w</math>, the area of <math>PQRS</math> can be expressed as the quadratic polynomial<br />
<br />
Area(<math>PQRS</math>) = <math>\alpha w - \beta \cdot w^2</math>.<br />
<br />
Then the coefficient <math>\beta = \frac{m}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>.<br />
<br />
==Solution 1==<br />
<br />
If <math>\omega = 25</math>, the area of rectangle <math>PQRS</math> is <math>0</math>, so<br />
<br />
<cmath>\alpha\omega - \beta\omega^2 = 25\alpha - 625\beta = 0</cmath><br />
<br />
and <math>\alpha = 25\beta</math>. If <math>\omega = \frac{25}{2}</math>, we can reflect <math>APQ</math> over PQ, <math>PBS</math> over <math>PS</math>, and <math>QCR</math> over <math>QR</math> to completely cover rectangle <math>PQRS</math>, so the area of <math>PQRS</math> is half the area of the triangle. Using Heron's formula, since <math>s = \frac{12 + 17 + 25}{2} = 27</math>, <br />
<br />
<cmath> [ABC] = \sqrt{27 \cdot 15 \cdot 10 \cdot 2} = 90</cmath><br />
<br />
so<br />
<br />
<cmath>45 = \alpha\omega - \beta\omega^2 = \frac{625}{2} \beta - \beta\frac{625}{4} = \beta\frac{625}{4}</cmath><br />
<br />
and <br />
<br />
<cmath>\beta = \frac{180}{625} = \frac{36}{125}</cmath><br />
<br />
so the answer is <math>m + n = 36 + 125 = \boxed{161}</math>.<br />
<br />
==Solution 2==<br />
<asy><br />
unitsize(20);<br />
pair A,B,C,E,F,P,Q,R,S;<br />
A=(48/5,36/5);<br />
B=(0,0);<br />
C=(25,0);<br />
E=(48/5,0);<br />
F=(48/5,18/5);<br />
P=(24/5,18/5);<br />
Q=(173/10,18/5);<br />
S=(24/5,0);<br />
R=(173/10,0);<br />
draw(A--B--C--cycle);<br />
draw(P--Q);<br />
draw(Q--R);<br />
draw(R--S);<br />
draw(S--P);<br />
draw(A--E,dashed);<br />
label("$A$",A,N);<br />
label("$B$",B,SW);<br />
label("$C$",C,SE);<br />
label("$E$",E,SE);<br />
label("$F$",F,NE);<br />
label("$P$",P,NW);<br />
label("$Q$",Q,NE);<br />
label("$R$",R,SE);<br />
label("$S$",S,SW);<br />
draw(rightanglemark(B,E,A,12));<br />
dot(E);<br />
dot(F);<br />
</asy><br />
<br />
Similar triangles can also solve the problem.<br />
<br />
First, solve for the area of the triangle. <math>[ABC] = 90</math>. This can be done by Heron's Formula or placing an <math>8-15-17</math> right triangle on <math>BC</math> and solving. (The <math>8</math> side would be collinear with line <math>AB</math>)<br />
<br />
After finding the area, solve for the altitude to <math>BC</math>. Let <math>E</math> be the intersection of the altitude from <math>A</math> and side <math>BC</math>. Then <math>AE = \frac{36}{5}</math>. <br />
Solving for <math>BE</math> using the Pythagorean Formula, we get <math>BE = \frac{48}{5}</math>. We then know that <math>CE = \frac{77}{5}</math>.<br />
<br />
Now consider the rectangle <math>PQRS</math>. Since <math>SR</math> is collinear with <math>BC</math> and parallel to <math>PQ</math>, <math>PQ</math> is parallel to <math>BC</math> meaning <math>\Delta APQ</math> is similar to <math>\Delta ABC</math>. <br />
<br />
Let <math>F</math> be the intersection between <math>AE</math> and <math>PQ</math>. By the similar triangles, we know that <math>\frac{PF}{FQ}=\frac{BE}{EC} = \frac{48}{77}</math>. Since <math>PF+FQ=PQ=\omega</math>. We can solve for <math>PF</math> and <math>FQ</math> in terms of <math>\omega</math>. We get that <math>PF=\frac{48}{125} \omega</math> and <math>FQ=\frac{77}{125} \omega</math>.<br />
<br />
Let's work with <math>PF</math>. We know that <math>PQ</math> is parallel to <math>BC</math> so <math>\Delta APF</math> is similar to <math>\Delta ABE</math>. We can set up the proportion:<br />
<br />
<math>\frac{AF}{PF}=\frac{AE}{BE}=\frac{3}{4}</math>. Solving for <math>AF</math>, <math>AF = \frac{3}{4} PF = \frac{3}{4} \cdot \frac{48}{125} \omega = \frac{36}{125} \omega</math>. <br />
<br />
We can solve for <math>PS</math> then since we know that <math>PS=FE</math> and <math>FE= AE - AF = \frac{36}{5} - \frac{36}{125} \omega</math>.<br />
<br />
Therefore, <math>[PQRS] = PQ \cdot PS = \omega (\frac{36}{5} - \frac{36}{125} \omega) = \frac{36}{5}\omega - \frac{36}{125} \omega^2</math>.<br />
<br />
This means that <math>\beta = \frac{36}{125} \Rightarrow (m,n) = (36,125) \Rightarrow m+n = \boxed{161}</math>.<br />
<br />
==Solution 3==<br />
Heron's Formula gives <math>[ABC] = \sqrt{27 \cdot 15 \cdot 10 \cdot 2} = 90,</math> so the altitude from <math>A</math> to <math>BC</math> has length <math>\dfrac{2[ABC]}{BC} = \dfrac{36}{5}.</math><br />
<br />
Now, draw a parallel to <math>AB</math> from <math>Q</math>, intersecting <math>BC</math> at <math>T</math>. Then <math>BT = w</math> in parallelogram <math>QPBT</math>, and so <math>CT = 25 - w</math>. Clearly, <math>CQT</math> and <math>CAB</math> are similar triangles, and so their altitudes have lengths proportional to their corresponding base sides, and so<br />
<cmath>\frac{QR}{\frac{36}{5}} = \frac{25 - w}{25}.</cmath><br />
Solving gives <math>[PQRS] = \dfrac{36}{5} \cdot \dfrac{25 - w}{25} = \dfrac{36w}{5} - \dfrac{36w^2}{125}</math>, so the answer is <math>36 + 125 = 161</math>.<br />
<br />
<br />
==Solution 4==<br />
Using the diagram from solution 2 above, label <math>AF</math> to be <math>h</math>. Through Heron's formula, the area of <math>ABC</math> turns out to be <math>90</math>, so using <math>AE</math> as the height and <math>BC</math> as the base yields <math>AE=\frac{36}{5}</math>. Now, through the use of similarity between <math>\triangle APQ</math> and <math>\triangle ABC</math>, you find <math>\frac{w}{25}=\frac{h}{36/5}</math>. Thus, <math>h=\frac{36w}{125}</math>. To find the height of the rectangle, subtract <math>h</math> from <math>\frac{36}{5}</math> to get <math>\left(\frac{36}{5}-\frac{36w}{125}\right)</math>, and multiply this by the other given side <math>w</math> to get <math>\frac{36w}{5}-\frac{36w^2}{125}</math> for the area of the rectangle. Finally, <math>36+125=\boxed{161}</math>.<br />
<br />
==See also==<br />
{{AIME box|year=2015|n=II|num-b=6|num-a=8}}<br />
{{MAA Notice}}</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Mathematics_websites&diff=70817Mathematics websites2015-06-18T22:46:06Z<p>Bluecarneal: /* Websites for high school students */</p>
<hr />
<div>There are many great '''Mathematics websites''' around the [[internet]]. Here we organize a list of those sites we feel are best for students with high interest in [[mathematics]]. Note that [[mathematics forums]] are listed and discussed seperately.<br />
<br />
<br />
<br />
== Internet Resource Websites ==<br />
<br />
* [http://archives.math.utk.edu/index.html Math Archives]<br />
* [http://www.math-atlas.org/ Math Atlas]<br />
<br />
<br />
== Websites for high school students ==<br />
<br />
* [http://www.pims.math.ca/pi/ Pi in the Sky] is a mathematics magazine for high school students.<br />
<br />
=== Websites for Olympiad students ===<br />
<br />
* [[Komal]] is a storied Hungarian [[math]] and [[physics]] journal. [http://www.komal.hu/info/bemutatkozas.e.shtml website].<br />
* [http://www.math.ust.hk/excalibur/ Mathematical Excalibur].<br />
* [http://reflections.awesomemath.org/ Mathematical Reflections] is a new online journal for Olympiad and collegiate mathematics.<br />
* [http://www.geometer.org/mathcircles/ Tom Davis's] site for [[math circles]] topics.<br />
* [http://mathworld.wolfram.com/ MathWorld] is a vast and well-maintained resource for math, science, and computer science professionals and students studying at a high level.<br />
<br />
== Websites for math enthusiasts ==<br />
<br />
* [[AoPS]] -- That's where you are now! [http://www.artofproblemsolving.com Home].<br />
* [[Cut-the-knot]], a.k.a. Interactive Mathematics Miscellany and Puzzles, is a large and amazing site put together by [[Alexander Bogomolny]]. It includes an enormous number of [[mathematics articles]] and [[math games]] that are well-designed for teaching mathematical concepts. [http://www.cut-the-knot.org/index.shtml website].<br />
* [[Mathematical Database]] contains lots of useful math stuff. [http://eng.mathdb.org/ website].<br />
* [http://www.geometer.org/mathcircles/ Tom Davis's] site for [[math circles]] topics.<br />
* [http://www.mathisfun.com Math is fun] site for math<br />
<br />
== Websites for Math Teachers ==<br />
* [http://www.ct4me.net/ CT4ME] is dedicated to promoting the use of [[technology]] in [[mathematics education]].<br />
<br />
<br />
<br />
== Websites for math history ==<br />
<br />
* [http://turnbull.dcs.st-and.ac.uk/history/index.html MacTudor History of Mathematics]<br />
* [[Wikipedia]] includes an enormous amount of information on the [http://en.wikipedia.org/wiki/History_of_math history of mathematics].<br />
<br />
<br />
== Websites for mathematicians ==<br />
<br />
* [http://mathworld.wolfram.com/ MathWorld] is a vast and well-maintained resource for math, science, and computer science professionals and students studying at a high level.<br />
* [[Wikipedia]] includes articles about noncontroversial, published [http://en.wikipedia.org/wiki/Mathematics mathematics].<br />
* [http://www.math-atlas.org/ Math Atlas]<br />
<br />
<br />
== See also ==<br />
<br />
* [[Mathematics competitions]]<br />
* [[Mathematics forums]]<br />
* [[Mathematics news]]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Fundamental_Theorem_of_Sato&diff=56613Fundamental Theorem of Sato2013-07-08T23:22:53Z<p>Bluecarneal: </p>
<hr />
<div>The Fundamental Theorem of Sato states the following:<br />
<br />
[[Naoki Sato]] is amazing. <br />
<br />
Proof: <br />
<br />
Assume, for contradiction, that Sato is not amazing. <br />
<br />
This is absurd. Therefore, Sato is amazing. <br />
<br />
'''QED'''</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=48249User:Bluecarneal2012-09-09T12:57:54Z<p>Bluecarneal: /* Problems Added but Didn't Post Myself (123) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (285)==<br />
===Problems Added but Didn't Post Myself (125)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1991&sid=85a6221e1d54bf1859580fb0643babba 1991 AHSME] (16-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=75&cid=93&year=1998&sid=c45fb074e6ab96b61490777b24e8baa9 1998 Hong Kong MO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=155&cid=81&year=2009 2009 Korean National Olympiad] (1-8)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=27&cid=103&year=2003&sid=35793b95be4f8ebb633939df3a4b3b06 2003 Bulgarian TST] (1-6)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
30,000th view (11/24/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=48248User:Bluecarneal2012-09-09T12:57:24Z<p>Bluecarneal: </p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (285)==<br />
===Problems Added but Didn't Post Myself (123)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1991&sid=85a6221e1d54bf1859580fb0643babba 1991 AHSME] (16-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=75&cid=93&year=1998&sid=c45fb074e6ab96b61490777b24e8baa9 1998 Hong Kong MO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=155&cid=81&year=2009 2009 Korean National Olympiad] (1-8)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=27&cid=103&year=2003&sid=35793b95be4f8ebb633939df3a4b3b06 2003 Bulgarian TST] (1-6)<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
30,000th view (11/24/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=48247User:Bluecarneal2012-09-09T12:47:40Z<p>Bluecarneal: </p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (279)==<br />
===Problems Added but Didn't Post Myself (119)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1991&sid=85a6221e1d54bf1859580fb0643babba 1991 AHSME] (16-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=75&cid=93&year=1998&sid=c45fb074e6ab96b61490777b24e8baa9 1998 Hong Kong MO] (1-4)<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=155&cid=81&year=2009 2009 Korean National Olympiad] (1-8)<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
30,000th view (11/24/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:FAQ&diff=45612AoPS Wiki:FAQ2012-03-17T22:54:13Z<p>Bluecarneal: /* What do some of the acronyms such as "OP" stand for? */</p>
<hr />
<div>{{shortcut|[[A:FAQ]]}}<br />
<br />
This is a community created list of Frequently Asked Questions about Art of Problem Solving. If you have a request to edit or add a question on this page, please make it [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=416&t=414129 here].<br />
<br />
== General ==<br />
<br />
<br />
==== Can I change my user name? ====<br />
<br />
:As indicated during the time of your registration, you are unable to change your username. If you accidentally registered using your real name and you are a relatively new user who has not been active on the site, we may be able to make the change for you. Due to technical reasons, abuse issues, and to prevent an overload of requests for changes of user name, we are not able to change your user name for any other reasons than accidentally using your real name.<br />
<br />
====What software does Art of Problem Solving use to run the website?====<br />
<br />
:* Forums: phpBB3<br />
:* Blog: User Blog Mod for phpBB3<br />
:* Wiki: MediaWiki<br />
:* Asymptote, Latex, and Geogebra are generated through their respective binary packages<br />
:* Videos: YouTube<br />
<br />
Note that as AoPS does not develop the above software, they are not responsible for the proper functioning of said software. Bug reports and feature requests should be sent to the appropriate developers of the above software. <br />
<br />
== Forums ==<br />
<br />
==== What do the stars under my username next to a forum post represent? ====<br />
<br />
:On the Art of Problem Solving website, under your username, you will find stars, as well as the name of one of the Millenium Problems. The number of stars you have, as well as the name of the Millenium Problem, depends on your post count. Here is the table that determines your "rank."<br />
<br />
:*0 - 19 New Member (Zero Stars)<br />
:*20 - 49 P versus NP (Half Star)<br />
:*50 - 99 Hodge Conjecture (One Star)<br />
:*100 - 249 Poincare Conjecture (Two Stars)<br />
:*250 - 499 Riemann Hypothesis (Two and Half stars) <br />
:*500 - 999 Yang Mills Theory (Three Stars)<br />
:*1000 - 2499 Navier-Stokes Equation (Four Stars)<br />
:*2500 - <math>\infty</math> Birch & Swinnerton Dyer. (Five Stars)<br />
:*Administrators have six stars.<br />
<br />
==== I got the message "You can not post at this time" when trying to post, why? ====<br />
<br />
:New users are not allowed to post messages with URLs and various other things. Once you have five posts you can post normally.<br />
<br />
==== If I make more posts, it means I'm a better user, right? ====<br />
<br />
:Absolutely not. Post quality is far more important than post quantity. Users making a lot of senseless posts are often considered worse users, or spammers.<br />
<br />
==== I have made some posts but my post count did not increase. Why? ====<br />
<br />
:When you post in some of the forums, such as the Test Forum, Mafia Forum, and the Fun Factory, it does not count towards your post count.<br />
<br />
==== When can I rate posts? ====<br />
<br />
:You will be able to rate posts after posting 10 messages.<br />
<br />
==== Who can see my post rating? ====<br />
<br />
:Only you, moderators, and administrators.<br />
<br />
==== How does AoPS select moderators? ====<br />
<br />
:When a new moderator is needed in the forums, AoPS administrators first check if any current moderators could serve as a moderator of the forum which needs a moderator. Should none be found, AoPS administrators and/or other moderators scour the forum looking for productive users. They may also ask for suggestions from other moderators or trusted users on the site. Once they have pinpointed a possible candidate based on their long term usage of the site, productive posts in the forum, and having no recent behavioral issues, that user is asked if he or she would like to moderate the forum. <br />
<br />
:Less active forums often have no moderator. Inappropriate posts should be reported by users and administrators will take appropriate action.<br />
<br />
:AoPS receives MANY requests to be a moderator. As they receive so many, it is possible that you won't get a response should you request to be one. Also, AoPS very rarely makes someone a mod for asking to be one, so '''please do not ask'''.<br />
<br />
==== I believe a post needs corrective action. What should I do? ====<br />
<br />
:If you believe a post needs moderative action, you may report it by clicking the "!" icon on the bottom-right corner of that post. If it's a minor mistake, you may want to PM the offending user instead and explain how they can make their post better. Usually, you shouldn't publicly post such things on a thread itself, which is called "backseat moderation" and is considered rude.<br />
<br />
==== How long of a non-commented thread is consider reviving? ====<br />
<br />
:If any post is still on-topic and isn't spammy or anything, it isn't considered reviving. The definition of reviving in the Games forum is 1 month. However, everyone has a different period of time that they consider reviving. In general, apply common sense.<br />
<br />
==== Someone is marking all my posts as spam, what should I do? ====<br />
<br />
:It happens to everyone. There's really not much you can do.<br />
<br />
==== Are posts marked spam more often than good? ====<br />
<br />
:No. The most common rating is 6 cubes. We understand that many posts are rated 1 when they shouldn't be. We also know that many posts are rated a 6 when they shouldn't be. It pretty much all averages out in the end. The best way to safeguard yourself is not to complain about it! In fact, most other members cannot see your rating. If you want to make a mark here, let your post quality do the talking.<br />
<br />
==== How do I post images? ====<br />
:There are limited attachment options for posts. Attachments have an overall size limit, and will be deleted as they get old. Attachments also may be deleted during any server move or software upgrade or change. You may instead wish to host images on another site and embed them in to your post using the [img] tags. The general format is [img]{url to image}[/img], excluding the braces. There are a number of image hosting sites, including:<br />
:* [http://imgur.com/ Imgur]<br />
:* [http://photobucket.com Photobucket]<br />
::*In thumbnail view<br />
:::*Hover over image and click the text box labeled IMG code. It will automatically copy to your clipboard<br />
:::*Paste to your message<br />
::*In image view<br />
:::*Look for the '''Links''' box which should appear at the right side of your screen<br />
:::*Click the box labeled IMG Code<br />
:::*Copy the text<br />
:::*Paste to your message<br />
:* [http://imageshack.com ImageShack]<br />
:* [http://minus.com minus.com]<br />
::*Go to image you wish to embed<br />
::*Click the share tab<br />
::*Copy the contents of the Forum Code text<br />
::*Paste to your message<br />
:* [http://bayfiles.com bayfiles.com]<br />
:* [http://picasaweb.google.com Picasa]<br />
:** This will vary by browser and OS, but the process is similar. The provided directions are for Firefox on Windows<br />
:** Go to the image you want to embed<br />
:** Right click on the image<br />
:** Select Copy Image Location<br />
:** Paste into your message, surrounding the pasted text with [img] and [/img] tags<br />
:* [http://www.flickr.com Flickr]<br />
<br />
See also:<br />
[http://www.artofproblemsolving.com/Wiki/index.php/Direct_Image_Link Direct Image Link]<br />
<br />
== Blogs ==<br />
==== How come I can't create a blog? ====<br />
One needs to have at least 10 posts in order to make a blog. <br />
<br />
== Contests ==<br />
==== Where can I find past contest questions and solutions? ====<br />
:In the [http://www.artofproblemsolving.com/Forum/resources.php Contests] section.<br />
<br />
==== How do I get problems onto the contest page? ====<br />
<br />
:Make a topic for each question in the appropriate forum, copy/paste the urls to the National Olympiad. Your problems may eventually be submitted into the Contest page.<br />
<br />
==== Who can I ask to add posts to the contests section? ====<br />
:Any one of the members in the the [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=group&g=417 RManagers] group.<br />
<br />
==== What are the guidelines for posting problems to be added to the contests section? ====<br />
:Refer to the [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=144&t=195579 guidelines in this post].<br />
<br />
==== Why is the wiki missing many contest questions? ====<br />
:Generally, it is because users have not yet posted them onto the wiki (translation difficulties, not having access to the actual problems, lack of interest, etc). If you have a copy, please post the problems in the Community Section! In some cases, however, problems may be missing due to copyright claims from maths organizations. See, for example, [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1391106#p1391106 this post].<br />
<br />
==== What if I find an error on a problem? ====<br />
Please post an accurate description of the problem in [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=426693 this thread]<br />
<br />
== LaTeX, Asymptote, GeoGebra ==<br />
==== What is LaTeX, and how do I use it? ====<br />
<br />
:<math>\LaTeX</math> is a typesetting markup language that is useful to produce properly formatted mathematical and scientific expressions.<br />
<br />
==== How can I download LaTeX to use on the forums? ====<br />
<br />
:There are no downloads necessary; the forums and the wiki render LaTeX commands between dollar signs. <br />
<br />
==== How can I download LaTeX for personal use? ====<br />
:You can download TeXstudio [http://texstudio.sourceforge.net here] or TeXnicCenter [http://www.texniccenter.org here]<br />
<br />
==== Where can I find a list of LaTeX commands? ====<br />
:See [[LaTeX:Symbols|here]].<br />
<br />
==== Where can I test LaTeX commands? ====<br />
<br />
:[[A:SAND|Sandbox]] or [http://www.artofproblemsolving.com/Resources/texer.php TeXeR]. <br />
<br />
==== Where can I find examples of Asymptote diagrams and code? ====<br />
<br />
:Search this wiki for the <tt><nowiki><asy></nowiki></tt> tag or the Forums for the <tt><nowiki>[asy]</nowiki></tt> tag. See also [[Asymptote:_Useful_commands_and_their_Output|these examples]] and [[Proofs without words|this article]] (click on the images to obtain the code).<br />
<br />
==== How can I draw 3D diagrams? ====<br />
<br />
:See [[Asymptote: 3D graphics]].<br />
<br />
==== What is the cse5 package? ==== <br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=149650 here]. The package contains a set of shorthand commands that implement the behavior of usual commands, for example <tt>D()</tt> for <tt>draw()</tt> and <tt>dot()</tt>, and so forth.<br />
<br />
==== What is the olympiad package? ====<br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 here]. The package contains a set of commands useful for drawing diagrams related to [[:Category:Olympiad Geometry Problems|olympiad geometry problems]].<br />
<br />
==== Can I convert diagrams from GeoGebra to other formats? ====<br />
:It is possible to export GeoGebra to [[Asymptote (Vector Graphics Language)|Asymptote]] (see [[User:Azjps/geogebra|here]]), PsTricks, and PGF/TikZ; and GeoGebra animations into .gif or video files. <br />
<br />
== AoPSWiki ==<br />
==== Is there a guide for wiki syntax? ====<br />
<br />
:See [http://en.wikipedia.org/wiki/Help:Wiki_markup wiki markup], [[AoPSWiki:Tutorial]], and [[Help:Contents]].<br />
<br />
==== What do I do if I see a mistake in the wiki? ====<br />
<br />
:Edit the page and correct the error! You can edit most pages on the wiki. Click the "edit" button on the right sidebar to edit a page.<br />
<br />
==== Why can't I edit the wiki? ====<br />
<br />
You must be a registered user to edit. To be registered, make sure you give a correct email, and activate your account.<br />
<br />
== Miscellaneous ==<br />
==== Is it possible to join the AoPS Staff? ====<br />
<br />
:Yes. Mr. Rusczyk will sometimes hire a small army of college students to work as interns. You must be at least in your second semester of your senior year and be legal to work in the U.S. (at least 16).<br />
<br />
==== What is the minimum age to be an assistant in an Art of Problem Solving class? ====<br />
<br />
:You must have graduated from high school, or at least be in the second term of your senior year.<br />
<br />
==What do some of the acronyms such as "OP" stand for?==<br />
*'''AFK'''- Away from keyboard<br />
*'''AoPS'''- Art of Problem Solving, the website you're on right now!<br />
*'''AMC'''- American Math Competititions<br />
*'''ATM'''- At the Moment<br />
*'''brb'''- Be right Back<br />
*'''EBWOP'''- Editing by way of post<br />
*'''FTW'''- For the Win, a game on AoPS<br />
*'''lol'''- Laugh Out Loud<br />
*'''MC'''- Mathcounts, a popular math contest for Middle School students.<br />
*'''OBC'''- Online by computer<br />
*'''OP'''- Original Poster<br />
*'''QED'''- Quod erat demonstrandum or Which was to be proven<br />
*'''QS&A'''- Questions, Suggestions, and Announcements Forum<br />
*'''V/LA'''- Vacation or Long Absence<br />
*'''wrt'''- With respect to<br />
<br />
== School ==<br />
<br />
==== What if I want to drop out of a class? ====<br />
:For any course with more than 2 classes, students can drop the course any time before the third class begins and receive a full refund. No drops are allowed after the third class has started. To drop the class, go to the My Classes section by clicking the My Classes link at the top-right of the website. Then find the area on the right side of the page that lets you drop the class. A refund will be processed within 10 business days.<br />
<br />
==== What if I miss a class? ====<br />
:There are classroom transcripts available under My Classes, available at the top right of the web site. You can view these transcripts in order to review any missed material. You can also ask questions on the class message board.<br />
<br />
==== Are there any audio and video during class? ====<br />
:There is no audio or video in the class. The classes are completely text based, in an interactive chat room environment, which allows students to ask questions at any time during the class. In addition to audio and video limiting interactivity, the technology isn't quite there yet for all students to be able to adequately receive streaming audio and video.<br />
<br />
====I feel like joining! What are my class choices? ====<br />
:[http://www.artofproblemsolving.com/School/classlist.php Class List] [http://www.artofproblemsolving.com/School/index.php?page=school.instructors Instructors List]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:FAQ&diff=45611AoPS Wiki:FAQ2012-03-17T22:53:46Z<p>Bluecarneal: Undo revision 45610 by Bluecarneal (talk)</p>
<hr />
<div>{{shortcut|[[A:FAQ]]}}<br />
<br />
This is a community created list of Frequently Asked Questions about Art of Problem Solving. If you have a request to edit or add a question on this page, please make it [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=416&t=414129 here].<br />
<br />
== General ==<br />
<br />
<br />
==== Can I change my user name? ====<br />
<br />
:As indicated during the time of your registration, you are unable to change your username. If you accidentally registered using your real name and you are a relatively new user who has not been active on the site, we may be able to make the change for you. Due to technical reasons, abuse issues, and to prevent an overload of requests for changes of user name, we are not able to change your user name for any other reasons than accidentally using your real name.<br />
<br />
====What software does Art of Problem Solving use to run the website?====<br />
<br />
:* Forums: phpBB3<br />
:* Blog: User Blog Mod for phpBB3<br />
:* Wiki: MediaWiki<br />
:* Asymptote, Latex, and Geogebra are generated through their respective binary packages<br />
:* Videos: YouTube<br />
<br />
Note that as AoPS does not develop the above software, they are not responsible for the proper functioning of said software. Bug reports and feature requests should be sent to the appropriate developers of the above software. <br />
<br />
== Forums ==<br />
<br />
==== What do the stars under my username next to a forum post represent? ====<br />
<br />
:On the Art of Problem Solving website, under your username, you will find stars, as well as the name of one of the Millenium Problems. The number of stars you have, as well as the name of the Millenium Problem, depends on your post count. Here is the table that determines your "rank."<br />
<br />
:*0 - 19 New Member (Zero Stars)<br />
:*20 - 49 P versus NP (Half Star)<br />
:*50 - 99 Hodge Conjecture (One Star)<br />
:*100 - 249 Poincare Conjecture (Two Stars)<br />
:*250 - 499 Riemann Hypothesis (Two and Half stars) <br />
:*500 - 999 Yang Mills Theory (Three Stars)<br />
:*1000 - 2499 Navier-Stokes Equation (Four Stars)<br />
:*2500 - <math>\infty</math> Birch & Swinnerton Dyer. (Five Stars)<br />
:*Administrators have six stars.<br />
<br />
==== I got the message "You can not post at this time" when trying to post, why? ====<br />
<br />
:New users are not allowed to post messages with URLs and various other things. Once you have five posts you can post normally.<br />
<br />
==== If I make more posts, it means I'm a better user, right? ====<br />
<br />
:Absolutely not. Post quality is far more important than post quantity. Users making a lot of senseless posts are often considered worse users, or spammers.<br />
<br />
==== I have made some posts but my post count did not increase. Why? ====<br />
<br />
:When you post in some of the forums, such as the Test Forum, Mafia Forum, and the Fun Factory, it does not count towards your post count.<br />
<br />
==== When can I rate posts? ====<br />
<br />
:You will be able to rate posts after posting 10 messages.<br />
<br />
==== Who can see my post rating? ====<br />
<br />
:Only you, moderators, and administrators.<br />
<br />
==== How does AoPS select moderators? ====<br />
<br />
:When a new moderator is needed in the forums, AoPS administrators first check if any current moderators could serve as a moderator of the forum which needs a moderator. Should none be found, AoPS administrators and/or other moderators scour the forum looking for productive users. They may also ask for suggestions from other moderators or trusted users on the site. Once they have pinpointed a possible candidate based on their long term usage of the site, productive posts in the forum, and having no recent behavioral issues, that user is asked if he or she would like to moderate the forum. <br />
<br />
:Less active forums often have no moderator. Inappropriate posts should be reported by users and administrators will take appropriate action.<br />
<br />
:AoPS receives MANY requests to be a moderator. As they receive so many, it is possible that you won't get a response should you request to be one. Also, AoPS very rarely makes someone a mod for asking to be one, so '''please do not ask'''.<br />
<br />
==== I believe a post needs corrective action. What should I do? ====<br />
<br />
:If you believe a post needs moderative action, you may report it by clicking the "!" icon on the bottom-right corner of that post. If it's a minor mistake, you may want to PM the offending user instead and explain how they can make their post better. Usually, you shouldn't publicly post such things on a thread itself, which is called "backseat moderation" and is considered rude.<br />
<br />
==== How long of a non-commented thread is consider reviving? ====<br />
<br />
:If any post is still on-topic and isn't spammy or anything, it isn't considered reviving. The definition of reviving in the Games forum is 1 month. However, everyone has a different period of time that they consider reviving. In general, apply common sense.<br />
<br />
==== Someone is marking all my posts as spam, what should I do? ====<br />
<br />
:It happens to everyone. There's really not much you can do.<br />
<br />
==== Are posts marked spam more often than good? ====<br />
<br />
:No. The most common rating is 6 cubes. We understand that many posts are rated 1 when they shouldn't be. We also know that many posts are rated a 6 when they shouldn't be. It pretty much all averages out in the end. The best way to safeguard yourself is not to complain about it! In fact, most other members cannot see your rating. If you want to make a mark here, let your post quality do the talking.<br />
<br />
==== How do I post images? ====<br />
:There are limited attachment options for posts. Attachments have an overall size limit, and will be deleted as they get old. Attachments also may be deleted during any server move or software upgrade or change. You may instead wish to host images on another site and embed them in to your post using the [img] tags. The general format is [img]{url to image}[/img], excluding the braces. There are a number of image hosting sites, including:<br />
:* [http://imgur.com/ Imgur]<br />
:* [http://photobucket.com Photobucket]<br />
::*In thumbnail view<br />
:::*Hover over image and click the text box labeled IMG code. It will automatically copy to your clipboard<br />
:::*Paste to your message<br />
::*In image view<br />
:::*Look for the '''Links''' box which should appear at the right side of your screen<br />
:::*Click the box labeled IMG Code<br />
:::*Copy the text<br />
:::*Paste to your message<br />
:* [http://imageshack.com ImageShack]<br />
:* [http://minus.com minus.com]<br />
::*Go to image you wish to embed<br />
::*Click the share tab<br />
::*Copy the contents of the Forum Code text<br />
::*Paste to your message<br />
:* [http://bayfiles.com bayfiles.com]<br />
:* [http://picasaweb.google.com Picasa]<br />
:** This will vary by browser and OS, but the process is similar. The provided directions are for Firefox on Windows<br />
:** Go to the image you want to embed<br />
:** Right click on the image<br />
:** Select Copy Image Location<br />
:** Paste into your message, surrounding the pasted text with [img] and [/img] tags<br />
:* [http://www.flickr.com Flickr]<br />
<br />
See also:<br />
[http://www.artofproblemsolving.com/Wiki/index.php/Direct_Image_Link Direct Image Link]<br />
<br />
== Blogs ==<br />
==== How come I can't create a blog? ====<br />
One needs to have at least 10 posts in order to make a blog. <br />
<br />
== Contests ==<br />
==== Where can I find past contest questions and solutions? ====<br />
:In the [http://www.artofproblemsolving.com/Forum/resources.php Contests] section.<br />
<br />
==== How do I get problems onto the contest page? ====<br />
<br />
:Make a topic for each question in the appropriate forum, copy/paste the urls to the National Olympiad. Your problems may eventually be submitted into the Contest page.<br />
<br />
==== Who can I ask to add posts to the contests section? ====<br />
:Any one of the members in the the [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=group&g=417 RManagers] group.<br />
<br />
==== What are the guidelines for posting problems to be added to the contests section? ====<br />
:Refer to the [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=144&t=195579 guidelines in this post].<br />
<br />
==== Why is the wiki missing many contest questions? ====<br />
:Generally, it is because users have not yet posted them onto the wiki (translation difficulties, not having access to the actual problems, lack of interest, etc). If you have a copy, please post the problems in the Community Section! In some cases, however, problems may be missing due to copyright claims from maths organizations. See, for example, [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1391106#p1391106 this post].<br />
<br />
==== What if I find an error on a problem? ====<br />
Please post an accurate description of the problem in [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=426693 this thread]<br />
<br />
== LaTeX, Asymptote, GeoGebra ==<br />
==== What is LaTeX, and how do I use it? ====<br />
<br />
:<math>\LaTeX</math> is a typesetting markup language that is useful to produce properly formatted mathematical and scientific expressions.<br />
<br />
==== How can I download LaTeX to use on the forums? ====<br />
<br />
:There are no downloads necessary; the forums and the wiki render LaTeX commands between dollar signs. <br />
<br />
==== How can I download LaTeX for personal use? ====<br />
:You can download TeXstudio [http://texstudio.sourceforge.net here] or TeXnicCenter [http://www.texniccenter.org here]<br />
<br />
==== Where can I find a list of LaTeX commands? ====<br />
:See [[LaTeX:Symbols|here]].<br />
<br />
==== Where can I test LaTeX commands? ====<br />
<br />
:[[A:SAND|Sandbox]] or [http://www.artofproblemsolving.com/Resources/texer.php TeXeR]. <br />
<br />
==== Where can I find examples of Asymptote diagrams and code? ====<br />
<br />
:Search this wiki for the <tt><nowiki><asy></nowiki></tt> tag or the Forums for the <tt><nowiki>[asy]</nowiki></tt> tag. See also [[Asymptote:_Useful_commands_and_their_Output|these examples]] and [[Proofs without words|this article]] (click on the images to obtain the code).<br />
<br />
==== How can I draw 3D diagrams? ====<br />
<br />
:See [[Asymptote: 3D graphics]].<br />
<br />
==== What is the cse5 package? ==== <br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=149650 here]. The package contains a set of shorthand commands that implement the behavior of usual commands, for example <tt>D()</tt> for <tt>draw()</tt> and <tt>dot()</tt>, and so forth.<br />
<br />
==== What is the olympiad package? ====<br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 here]. The package contains a set of commands useful for drawing diagrams related to [[:Category:Olympiad Geometry Problems|olympiad geometry problems]].<br />
<br />
==== Can I convert diagrams from GeoGebra to other formats? ====<br />
:It is possible to export GeoGebra to [[Asymptote (Vector Graphics Language)|Asymptote]] (see [[User:Azjps/geogebra|here]]), PsTricks, and PGF/TikZ; and GeoGebra animations into .gif or video files. <br />
<br />
== AoPSWiki ==<br />
==== Is there a guide for wiki syntax? ====<br />
<br />
:See [http://en.wikipedia.org/wiki/Help:Wiki_markup wiki markup], [[AoPSWiki:Tutorial]], and [[Help:Contents]].<br />
<br />
==== What do I do if I see a mistake in the wiki? ====<br />
<br />
:Edit the page and correct the error! You can edit most pages on the wiki. Click the "edit" button on the right sidebar to edit a page.<br />
<br />
==== Why can't I edit the wiki? ====<br />
<br />
You must be a registered user to edit. To be registered, make sure you give a correct email, and activate your account.<br />
<br />
== Miscellaneous ==<br />
==== Is it possible to join the AoPS Staff? ====<br />
<br />
:Yes. Mr. Rusczyk will sometimes hire a small army of college students to work as interns. You must be at least in your second semester of your senior year and be legal to work in the U.S. (at least 16).<br />
<br />
==== What is the minimum age to be an assistant in an Art of Problem Solving class? ====<br />
<br />
:You must have graduated from high school, or at least be in the second term of your senior year.<br />
<br />
==What do some of the acronyms such as "OP" stand for?==<br />
*'''AFK'''- Away from keyboard<br />
*'''AoPS'''- Art of Problem Solving, the website you're on right now!<br />
*'''AMC'''- American Math Competititions<br />
*'''ATM'''- At the Moment<br />
*'''brb'''- Be right Back<br />
*'''EBWOP'''- EEditing by way of post<br />
*'''FTW'''- For the Win, a game on AoPS<br />
*'''lol'''- Laugh Out Loud<br />
*'''MC'''- Mathcounts, a popular math contest for Middle School students.<br />
*'''OBC'''- Online by computer<br />
*'''OP'''- Original Poster<br />
*'''QED'''- Quod erat demonstrandum or Which was to be proven<br />
*'''QS&A'''- Questions, Suggestions, and Announcements Forum<br />
*'''V/LA'''- Vacation or Long Absence<br />
*'''wrt'''- With respect to<br />
<br />
== School ==<br />
<br />
==== What if I want to drop out of a class? ====<br />
:For any course with more than 2 classes, students can drop the course any time before the third class begins and receive a full refund. No drops are allowed after the third class has started. To drop the class, go to the My Classes section by clicking the My Classes link at the top-right of the website. Then find the area on the right side of the page that lets you drop the class. A refund will be processed within 10 business days.<br />
<br />
==== What if I miss a class? ====<br />
:There are classroom transcripts available under My Classes, available at the top right of the web site. You can view these transcripts in order to review any missed material. You can also ask questions on the class message board.<br />
<br />
==== Are there any audio and video during class? ====<br />
:There is no audio or video in the class. The classes are completely text based, in an interactive chat room environment, which allows students to ask questions at any time during the class. In addition to audio and video limiting interactivity, the technology isn't quite there yet for all students to be able to adequately receive streaming audio and video.<br />
<br />
====I feel like joining! What are my class choices? ====<br />
:[http://www.artofproblemsolving.com/School/classlist.php Class List] [http://www.artofproblemsolving.com/School/index.php?page=school.instructors Instructors List]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:FAQ&diff=45610AoPS Wiki:FAQ2012-03-17T22:52:57Z<p>Bluecarneal: /* What do some of the acronyms such as "OP" stand for? */</p>
<hr />
<div>{{shortcut|[[A:FAQ]]}}<br />
<br />
This is a community created list of Frequently Asked Questions about Art of Problem Solving. If you have a request to edit or add a question on this page, please make it [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=416&t=414129 here].<br />
<br />
== General ==<br />
<br />
<br />
==== Can I change my user name? ====<br />
<br />
:As indicated during the time of your registration, you are unable to change your username. If you accidentally registered using your real name and you are a relatively new user who has not been active on the site, we may be able to make the change for you. Due to technical reasons, abuse issues, and to prevent an overload of requests for changes of user name, we are not able to change your user name for any other reasons than accidentally using your real name.<br />
<br />
====What software does Art of Problem Solving use to run the website?====<br />
<br />
:* Forums: phpBB3<br />
:* Blog: User Blog Mod for phpBB3<br />
:* Wiki: MediaWiki<br />
:* Asymptote, Latex, and Geogebra are generated through their respective binary packages<br />
:* Videos: YouTube<br />
<br />
Note that as AoPS does not develop the above software, they are not responsible for the proper functioning of said software. Bug reports and feature requests should be sent to the appropriate developers of the above software. <br />
<br />
== Forums ==<br />
<br />
==== What do the stars under my username next to a forum post represent? ====<br />
<br />
:On the Art of Problem Solving website, under your username, you will find stars, as well as the name of one of the Millenium Problems. The number of stars you have, as well as the name of the Millenium Problem, depends on your post count. Here is the table that determines your "rank."<br />
<br />
:*0 - 19 New Member (Zero Stars)<br />
:*20 - 49 P versus NP (Half Star)<br />
:*50 - 99 Hodge Conjecture (One Star)<br />
:*100 - 249 Poincare Conjecture (Two Stars)<br />
:*250 - 499 Riemann Hypothesis (Two and Half stars) <br />
:*500 - 999 Yang Mills Theory (Three Stars)<br />
:*1000 - 2499 Navier-Stokes Equation (Four Stars)<br />
:*2500 - <math>\infty</math> Birch & Swinnerton Dyer. (Five Stars)<br />
:*Administrators have six stars.<br />
<br />
==== I got the message "You can not post at this time" when trying to post, why? ====<br />
<br />
:New users are not allowed to post messages with URLs and various other things. Once you have five posts you can post normally.<br />
<br />
==== If I make more posts, it means I'm a better user, right? ====<br />
<br />
:Absolutely not. Post quality is far more important than post quantity. Users making a lot of senseless posts are often considered worse users, or spammers.<br />
<br />
==== I have made some posts but my post count did not increase. Why? ====<br />
<br />
:When you post in some of the forums, such as the Test Forum, Mafia Forum, and the Fun Factory, it does not count towards your post count.<br />
<br />
==== When can I rate posts? ====<br />
<br />
:You will be able to rate posts after posting 10 messages.<br />
<br />
==== Who can see my post rating? ====<br />
<br />
:Only you, moderators, and administrators.<br />
<br />
==== How does AoPS select moderators? ====<br />
<br />
:When a new moderator is needed in the forums, AoPS administrators first check if any current moderators could serve as a moderator of the forum which needs a moderator. Should none be found, AoPS administrators and/or other moderators scour the forum looking for productive users. They may also ask for suggestions from other moderators or trusted users on the site. Once they have pinpointed a possible candidate based on their long term usage of the site, productive posts in the forum, and having no recent behavioral issues, that user is asked if he or she would like to moderate the forum. <br />
<br />
:Less active forums often have no moderator. Inappropriate posts should be reported by users and administrators will take appropriate action.<br />
<br />
:AoPS receives MANY requests to be a moderator. As they receive so many, it is possible that you won't get a response should you request to be one. Also, AoPS very rarely makes someone a mod for asking to be one, so '''please do not ask'''.<br />
<br />
==== I believe a post needs corrective action. What should I do? ====<br />
<br />
:If you believe a post needs moderative action, you may report it by clicking the "!" icon on the bottom-right corner of that post. If it's a minor mistake, you may want to PM the offending user instead and explain how they can make their post better. Usually, you shouldn't publicly post such things on a thread itself, which is called "backseat moderation" and is considered rude.<br />
<br />
==== How long of a non-commented thread is consider reviving? ====<br />
<br />
:If any post is still on-topic and isn't spammy or anything, it isn't considered reviving. The definition of reviving in the Games forum is 1 month. However, everyone has a different period of time that they consider reviving. In general, apply common sense.<br />
<br />
==== Someone is marking all my posts as spam, what should I do? ====<br />
<br />
:It happens to everyone. There's really not much you can do.<br />
<br />
==== Are posts marked spam more often than good? ====<br />
<br />
:No. The most common rating is 6 cubes. We understand that many posts are rated 1 when they shouldn't be. We also know that many posts are rated a 6 when they shouldn't be. It pretty much all averages out in the end. The best way to safeguard yourself is not to complain about it! In fact, most other members cannot see your rating. If you want to make a mark here, let your post quality do the talking.<br />
<br />
==== How do I post images? ====<br />
:There are limited attachment options for posts. Attachments have an overall size limit, and will be deleted as they get old. Attachments also may be deleted during any server move or software upgrade or change. You may instead wish to host images on another site and embed them in to your post using the [img] tags. The general format is [img]{url to image}[/img], excluding the braces. There are a number of image hosting sites, including:<br />
:* [http://imgur.com/ Imgur]<br />
:* [http://photobucket.com Photobucket]<br />
::*In thumbnail view<br />
:::*Hover over image and click the text box labeled IMG code. It will automatically copy to your clipboard<br />
:::*Paste to your message<br />
::*In image view<br />
:::*Look for the '''Links''' box which should appear at the right side of your screen<br />
:::*Click the box labeled IMG Code<br />
:::*Copy the text<br />
:::*Paste to your message<br />
:* [http://imageshack.com ImageShack]<br />
:* [http://minus.com minus.com]<br />
::*Go to image you wish to embed<br />
::*Click the share tab<br />
::*Copy the contents of the Forum Code text<br />
::*Paste to your message<br />
:* [http://bayfiles.com bayfiles.com]<br />
:* [http://picasaweb.google.com Picasa]<br />
:** This will vary by browser and OS, but the process is similar. The provided directions are for Firefox on Windows<br />
:** Go to the image you want to embed<br />
:** Right click on the image<br />
:** Select Copy Image Location<br />
:** Paste into your message, surrounding the pasted text with [img] and [/img] tags<br />
:* [http://www.flickr.com Flickr]<br />
<br />
See also:<br />
[http://www.artofproblemsolving.com/Wiki/index.php/Direct_Image_Link Direct Image Link]<br />
<br />
== Blogs ==<br />
==== How come I can't create a blog? ====<br />
One needs to have at least 10 posts in order to make a blog. <br />
<br />
== Contests ==<br />
==== Where can I find past contest questions and solutions? ====<br />
:In the [http://www.artofproblemsolving.com/Forum/resources.php Contests] section.<br />
<br />
==== How do I get problems onto the contest page? ====<br />
<br />
:Make a topic for each question in the appropriate forum, copy/paste the urls to the National Olympiad. Your problems may eventually be submitted into the Contest page.<br />
<br />
==== Who can I ask to add posts to the contests section? ====<br />
:Any one of the members in the the [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=group&g=417 RManagers] group.<br />
<br />
==== What are the guidelines for posting problems to be added to the contests section? ====<br />
:Refer to the [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=144&t=195579 guidelines in this post].<br />
<br />
==== Why is the wiki missing many contest questions? ====<br />
:Generally, it is because users have not yet posted them onto the wiki (translation difficulties, not having access to the actual problems, lack of interest, etc). If you have a copy, please post the problems in the Community Section! In some cases, however, problems may be missing due to copyright claims from maths organizations. See, for example, [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1391106#p1391106 this post].<br />
<br />
==== What if I find an error on a problem? ====<br />
Please post an accurate description of the problem in [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=426693 this thread]<br />
<br />
== LaTeX, Asymptote, GeoGebra ==<br />
==== What is LaTeX, and how do I use it? ====<br />
<br />
:<math>\LaTeX</math> is a typesetting markup language that is useful to produce properly formatted mathematical and scientific expressions.<br />
<br />
==== How can I download LaTeX to use on the forums? ====<br />
<br />
:There are no downloads necessary; the forums and the wiki render LaTeX commands between dollar signs. <br />
<br />
==== How can I download LaTeX for personal use? ====<br />
:You can download TeXstudio [http://texstudio.sourceforge.net here] or TeXnicCenter [http://www.texniccenter.org here]<br />
<br />
==== Where can I find a list of LaTeX commands? ====<br />
:See [[LaTeX:Symbols|here]].<br />
<br />
==== Where can I test LaTeX commands? ====<br />
<br />
:[[A:SAND|Sandbox]] or [http://www.artofproblemsolving.com/Resources/texer.php TeXeR]. <br />
<br />
==== Where can I find examples of Asymptote diagrams and code? ====<br />
<br />
:Search this wiki for the <tt><nowiki><asy></nowiki></tt> tag or the Forums for the <tt><nowiki>[asy]</nowiki></tt> tag. See also [[Asymptote:_Useful_commands_and_their_Output|these examples]] and [[Proofs without words|this article]] (click on the images to obtain the code).<br />
<br />
==== How can I draw 3D diagrams? ====<br />
<br />
:See [[Asymptote: 3D graphics]].<br />
<br />
==== What is the cse5 package? ==== <br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=149650 here]. The package contains a set of shorthand commands that implement the behavior of usual commands, for example <tt>D()</tt> for <tt>draw()</tt> and <tt>dot()</tt>, and so forth.<br />
<br />
==== What is the olympiad package? ====<br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 here]. The package contains a set of commands useful for drawing diagrams related to [[:Category:Olympiad Geometry Problems|olympiad geometry problems]].<br />
<br />
==== Can I convert diagrams from GeoGebra to other formats? ====<br />
:It is possible to export GeoGebra to [[Asymptote (Vector Graphics Language)|Asymptote]] (see [[User:Azjps/geogebra|here]]), PsTricks, and PGF/TikZ; and GeoGebra animations into .gif or video files. <br />
<br />
== AoPSWiki ==<br />
==== Is there a guide for wiki syntax? ====<br />
<br />
:See [http://en.wikipedia.org/wiki/Help:Wiki_markup wiki markup], [[AoPSWiki:Tutorial]], and [[Help:Contents]].<br />
<br />
==== What do I do if I see a mistake in the wiki? ====<br />
<br />
:Edit the page and correct the error! You can edit most pages on the wiki. Click the "edit" button on the right sidebar to edit a page.<br />
<br />
==== Why can't I edit the wiki? ====<br />
<br />
You must be a registered user to edit. To be registered, make sure you give a correct email, and activate your account.<br />
<br />
== Miscellaneous ==<br />
==== Is it possible to join the AoPS Staff? ====<br />
<br />
:Yes. Mr. Rusczyk will sometimes hire a small army of college students to work as interns. You must be at least in your second semester of your senior year and be legal to work in the U.S. (at least 16).<br />
<br />
==== What is the minimum age to be an assistant in an Art of Problem Solving class? ====<br />
<br />
:You must have graduated from high school, or at least be in the second term of your senior year.<br />
<br />
==What do some of the acronyms such as "OP" stand for?==<br />
*'''AFK'''- Away from keyboard<br />
*'''AoPS'''- Art of Problem Solving, the website you're on right now!<br />
*'''AMC'''- American Math Competititions<br />
*'''ATM'''- At the Moment<br />
*'''brb'''- Be right Back<br />
*'''EBWOP'''- Editing by way of post<br />
*'''FTW'''- For the Win, a game on AoPS<br />
*'''lol'''- Laugh Out Loud<br />
*'''MC'''- Mathcounts, a popular math contest for Middle School students.<br />
*'''OBC'''- Online by computer<br />
*"'OBP'" - Online by phone<br />
*'''OP'''- Original Poster<br />
*'''QED'''- Quod erat demonstrandum or Which was to be proven<br />
*'''QS&A'''- Questions, Suggestions, and Announcements Forum<br />
*'''V/LA'''- Vacation or Long Absence<br />
*"'WLOG'" - Without loss of generality<br />
*'''wrt'''- With respect to<br />
<br />
== School ==<br />
<br />
==== What if I want to drop out of a class? ====<br />
:For any course with more than 2 classes, students can drop the course any time before the third class begins and receive a full refund. No drops are allowed after the third class has started. To drop the class, go to the My Classes section by clicking the My Classes link at the top-right of the website. Then find the area on the right side of the page that lets you drop the class. A refund will be processed within 10 business days.<br />
<br />
==== What if I miss a class? ====<br />
:There are classroom transcripts available under My Classes, available at the top right of the web site. You can view these transcripts in order to review any missed material. You can also ask questions on the class message board.<br />
<br />
==== Are there any audio and video during class? ====<br />
:There is no audio or video in the class. The classes are completely text based, in an interactive chat room environment, which allows students to ask questions at any time during the class. In addition to audio and video limiting interactivity, the technology isn't quite there yet for all students to be able to adequately receive streaming audio and video.<br />
<br />
====I feel like joining! What are my class choices? ====<br />
:[http://www.artofproblemsolving.com/School/classlist.php Class List] [http://www.artofproblemsolving.com/School/index.php?page=school.instructors Instructors List]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Pre-Olympiad_Level_Tournament_By_Mathtime&diff=44164Pre-Olympiad Level Tournament By Mathtime2012-01-07T20:06:59Z<p>Bluecarneal: Fixed typo, LaTeX</p>
<hr />
<div>=Problem 1=<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=456734 <math>\boxed{1}</math>]<br />
<br />
Suppose we have a sequence, with the first term equal to <math>a_1</math>, with <math>a_1>0</math>, an a second term of <math>3</math> and each term after that, <math>a_n</math> equal to <math>F_{a_{n-1}*a_{n-2}}</math>, which is the <math>a_{n-1}*a_{n-2}</math>'th Fibonacci number. Assume that <math>a_k</math> is always an integer in this problem, and that <math>k</math> must always be an integer in this problem.<br />
<br />
Find (with proof) all integers <math>a_1</math>, such that this sequence has the integer <math>832040</math> in it.<br />
<br />
=Problem 2=<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=456747 <math>\boxed{2}</math>]<br />
<br />
In a cyclic quadrilateral with sides <math>AB, BC, CD, AC</math> prove that:<br />
<math>(AB+BC+CD+AD)^4\ge 64(-(AB)(CD)-(BC)(AD)+2(AC)(BD))^2-64((AB)^2(CD)^2-2(AB)(BC)(CD)(AD)+(BC)^2(AD)^2)</math><br />
<br />
=Problem 3=<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=456748 <math>\boxed{3}</math>]<br />
<br />
Prove that there is no positive integers <math>k</math> such that <math>\frac{(x^2+y^2+xz)+x^m*y^z}{x^2-y^2}=3+kx+ky\ \forall x,y \in \mathbb{N}</math>, and this equation must satify for all <math>x</math> and <math>y</math>, and <math>m</math> and <math>z</math> are positive integers.</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=44149User:Bluecarneal2012-01-05T15:50:47Z<p>Bluecarneal: /* RManaging (267) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (271)==<br />
===Problems Added but Didn't Post Myself (111)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1991&sid=85a6221e1d54bf1859580fb0643babba 1991 AHSME] (16-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=75&cid=93&year=1998&sid=c45fb074e6ab96b61490777b24e8baa9 1998 Hong Kong MO] (1-4)<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
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50th entry (1/10/11)<br />
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200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
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1500th view:(1/14/11)<br />
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300th comment (1/16/11)<br />
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2000th view (1/17/11)<br />
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2500th view (1/19/11)<br />
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3000th view (1/23/11)<br />
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4000th view (2/1/11)<br />
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500th comment (2/3/11)<br />
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5000th view (2/7/11)<br />
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6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
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600th comment (2/17/11)<br />
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40th update (2/21/11)<br />
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7000th view (2/23/11)<br />
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8000th view (2/28/11)<br />
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700th comment (3/4/11)<br />
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50th update (3/5/11)<br />
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9000th view (3/7/11)<br />
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10000th view (3/13/11)<br />
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300th entry (3/14/11)<br />
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15,000th view (4/11/11)<br />
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400th entry (4/28/11)<br />
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1,000th Comment (5/23/11)<br />
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20,000th view (6/13/11)<br />
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25,000th view (8/25/11)<br />
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30,000th view (11/24/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=AoPS_Wiki:FAQ&diff=43777AoPS Wiki:FAQ2011-12-18T23:24:07Z<p>Bluecarneal: /* Why is the wiki is missing many contest questions? */</p>
<hr />
<div>{{shortcut|[[A:FAQ]]}}<br />
<br />
This is a community created list of Frequently Asked Questions about Art of Problem Solving. If you have a request to edit or add a question on this page, please make it [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=416&t=414129 here].<br />
<br />
== General ==<br />
<br />
<br />
==== Can I change my user name? ====<br />
<br />
:As indicated during the time of your registration, you are unable to change your username. If you accidentally registered using your real name and you are a relatively new user who has not been active on the site, we may be able to make the change for you. Due to technical reasons, abuse issues, and to prevent an overload of requests for changes of user name, we are not able to change your user name for any other reasons than accidentally using your real name.<br />
<br />
====What software does Art of Problem Solving use to run the website?====<br />
<br />
:* Forums: phpBB3<br />
:* Blog: User Blog Mod for phpBB3<br />
:* Wiki: MediaWiki<br />
:* Asymptote, Latex, and Geogebra are generated through their respective binary packages<br />
:* Videos: YouTube<br />
<br />
Note that as AoPS does not develop the above software, they are not responsible for the proper functioning of said software. Bug reports and feature requests should be sent to the appropriate developers of the above software. <br />
<br />
== Forums ==<br />
<br />
==== What do the stars under my username next to a forum post represent? ====<br />
<br />
:On the Art of Problem Solving website, under your username, you will find stars, as well as the name of one of the Millenium Problems. The number of stars you have, as well as the name of the Millenium Problem, depends on your post count. Here is the table that determines your "rank."<br />
<br />
:*0 - 19 New Member (Zero Stars)<br />
:*20 - 49 P versus NP (Half Star)<br />
:*50 - 99 Hodge Conjecture (One Star)<br />
:*100 - 249 Poincare Conjecture (Two Stars)<br />
:*250 - 499 Riemann Hypothesis (Two and Half stars) <br />
:*500 - 999 Yang Mills Theory (Three Stars)<br />
:*1000 - 2499 Navier-Stokes Equation (Four Stars)<br />
:*2500 - <math>\infty</math> Birch & Swinnerton Dyer. (Five Stars)<br />
:*Administrators have six stars.<br />
<br />
==== I got the message "You can not post at this time" when trying to post, why? ====<br />
<br />
:New users are not allowed to post messages with URLs and various other things. Once you have five posts you can post normally.<br />
<br />
==== If I make more posts, it means I'm a better user, right? ====<br />
<br />
:Absolutely not. Post quality is far more important than post quantity. Users making a lot of senseless posts are often considered worse users, or spammers.<br />
<br />
==== I have made some posts but my post count did not increase. Why? ====<br />
<br />
:When you post in some of the forums, such as the Test Forum, Mafia Forum, and the Fun Factory, it does not count towards your post count.<br />
<br />
==== Who can see my post rating? ====<br />
<br />
:Only you, moderators, and administrators.<br />
<br />
==== How does AoPS select moderators? ====<br />
<br />
:When a new moderator is needed in the forums, AoPS administrators first check if any current moderators could serve as a moderator of the forum which needs a moderator. Should none be found, AoPS administrators and/or other moderators scour the forum looking for productive users. They may also ask for suggestions from other moderators or trusted users on the site. Once they have pinpointed a possible candidate based on their long term usage of the site, productive posts in the forum, and having no recent behavioral issues, that user is asked if he or she would like to moderate the forum. <br />
<br />
:Less active forums often have no moderator. Inappropriate posts should be reported by users and administrators will take appropriate action.<br />
<br />
:AoPS receives MANY requests to be a moderator. As they receive so many, it is possible that you won't get a response should you request to be one. Also, AoPS very rarely makes someone a mod for asking to be one, so '''please do not ask'''.<br />
<br />
==== I believe a post needs corrective action. What should I do? ====<br />
<br />
:If you believe a post needs moderative action, you may report it by clicking the "!" icon on the bottom-right corner of that post. If it's a minor mistake, you may want to PM the offending user instead and explain how they can make their post better. Usually, you shouldn't publicly post such things on a thread itself, which is called "backseat moderation" and is considered rude.<br />
<br />
==== How long of a not commented post is consider reviving? ====<br />
<br />
:If any post is still on-topic and isn't spammy or anything, it isn't considered reviving. The definition of reviving in the Games forum is 1 month. However, everyone has a different period of time that they consider reviving. In general, apply common sense.<br />
<br />
==== Someone is marking all my posts as spam, what should I do? ====<br />
<br />
:It happens to everyone. There's really not much you can do.<br />
<br />
==== Are posts marked spam more often than good? ====<br />
<br />
:No. The most common rating is 6 cubes. We understand that many posts are rated 1 when they shouldn't be. We also know that many posts are rated a 6 when they shouldn't be. It pretty much all averages out in the end.The best way to safeguard yourself is not to complain about it!In fact ,most other members cannot see your rating.If you want to to make a mark here,let your post quality do the talking.<br />
<br />
==== How can I post images? ====<br />
:There are limited attachment options for posts. Attachments have an overall size limit, and will be deleted as the get old. Attachments also may be deleted during any server move or software upgrade or change. You may instead wish to host images on another site and embed them in to your post using the [img] tags. The general format is [img]{url to image}[/img], excluding the braces. There are a number of image hosting sites, including:<br />
:* [http://imgur.com/ Imgur]<br />
:* [http://photobucket.com Photobucket]<br />
::*In thumbnail view<br />
:::*Hover over image and click the text box labeled IMG code. It will automatically copy to your clipboard<br />
:::*Paste to your message<br />
::*In image view<br />
:::*Look for the '''Links''' box which should appear at the right side of your screen<br />
:::*Click the box labeled IMG Code<br />
:::*Copy the text<br />
:::*Paste to your message<br />
:* [http://imageshack.com ImageShack]<br />
:* [http://minus.com minus.com]<br />
::*Go to image you wish to embed<br />
::*Click the share tab<br />
::*Copy the contents of the Forum Code text<br />
::*Paste to your message<br />
:* [http://bayfiles.com bayfiles.com]<br />
:* [http://picasaweb.google.com Picasa]<br />
:** This will vary by browser and OS, but the process is similar. The provided directions are for Firefox on Windows<br />
:** Go to the image you want to embed<br />
:** Right click on the image<br />
:** Select Copy Image Location<br />
:** Paste into your message, surrounding the pasted text with [img] and [/img] tags<br />
:* [http://www.flickr.com Flickr]<br />
<br />
See also:<br />
[http://www.artofproblemsolving.com/Wiki/index.php/Direct_Image_Link Direct Image Link]<br />
<br />
== Blogs ==<br />
==== How come I can't create a blog? ====<br />
One needs to have at least 10 posts in order to make a blog. <br />
<br />
== Contests ==<br />
==== Where can I find past contest questions and solutions? ====<br />
:In the [http://www.artofproblemsolving.com/Forum/resources.php Contests] section.<br />
<br />
==== How do I get problems onto the contest page? ====<br />
<br />
:Make a topic for each question in the appropriate forum, copy/paste the urls to the National Olympiad. Your problems may eventually be submitted into the Contest page.<br />
<br />
==== Who can I ask to add posts to the contests section? ====<br />
:Any one of the members in the the [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=group&g=417 RManagers] group.<br />
<br />
==== What are the guidelines for posting problems to be added to the contests section? ====<br />
:Refer to the [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=144&t=195579 guidelines in this post].<br />
<br />
==== Why is the wiki missing many contest questions? ====<br />
:Generally, it is because users have not yet posted them onto the wiki (translation difficulties, not having access to the actual problems, lack of interest, etc). If you have a copy, please post the problems in the Community Section! In some cases, however, problems may be missing due to copyright claims from maths organizations. See, for example, [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1391106#p1391106 this post].<br />
<br />
==== What if I find an error on a problem? ====<br />
Please post an accurate description of the problem in [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=133&t=426693 this thread]<br />
<br />
== LaTeX, Asymptote, GeoGebra ==<br />
==== What is LaTeX, and how do I use it? ====<br />
<br />
:<math>\LaTeX</math> is a typesetting markup language that is useful to produce properly formatted mathematical and scientific expressions.<br />
<br />
==== How can I download LaTeX to use on the forums? ====<br />
<br />
:There are no downloads necessary; the forums and the wiki render LaTeX commands between dollar signs. <br />
<br />
==== How can I download LaTeX for personal use? ====<br />
:You can download TeXstudio [http://texstudio.sourceforge.net here] or TeXnicCenter [http://www.texniccenter.org here]<br />
<br />
==== Where can I find a list of LaTeX commands? ====<br />
:See [[LaTeX:Symbols|here]].<br />
<br />
==== Where can I test LaTeX commands? ====<br />
<br />
:[[A:SAND|Sandbox]] or [http://www.artofproblemsolving.com/Resources/texer.php TeXeR]. <br />
<br />
==== Where can I find examples of Asymptote diagrams and code? ====<br />
<br />
:Search this wiki for the <tt><nowiki><asy></nowiki></tt> tag or the Forums for the <tt><nowiki>[asy]</nowiki></tt> tag. See also [[Asymptote:_Useful_commands_and_their_Output|these examples]] and [[Proofs without words|this article]] (click on the images to obtain the code).<br />
<br />
==== How can I draw 3D diagrams? ====<br />
<br />
:See [[Asymptote: 3D graphics]].<br />
<br />
==== What is the cse5 package? ==== <br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=149650 here]. The package contains a set of shorthand commands that implement the behavior of usual commands, for example <tt>D()</tt> for <tt>draw()</tt> and <tt>dot()</tt>, and so forth.<br />
<br />
==== What is the olympiad package? ====<br />
<br />
:See [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=519&t=165767 here]. The package contains a set of commands useful for drawing diagrams related to [[:Category:Olympiad Geometry Problems|olympiad geometry problems]].<br />
<br />
==== Can I convert diagrams from GeoGebra to other formats? ====<br />
:It is possible to export GeoGebra to [[Asymptote (Vector Graphics Language)|Asymptote]] (see [[User:Azjps/geogebra|here]]), PsTricks, and PGF/TikZ; and GeoGebra animations into .gif or video files. <br />
<br />
== AoPSWiki ==<br />
==== Is there a guide for wiki syntax? ====<br />
<br />
:See [http://en.wikipedia.org/wiki/Help:Wiki_markup wiki markup], [[AoPSWiki:Tutorial]], and [[Help:Contents]].<br />
<br />
==== What do I do if I see a mistake in the wiki? ====<br />
<br />
:Edit the page and correct the error! You can edit most pages on the wiki. Click the "edit" button on the right sidebar to edit a page.<br />
<br />
== Miscellaneous ==<br />
==== Is it possible to join the AoPS Staff? ====<br />
<br />
:Yes. Mr. Rusczyk will sometimes hire a small army of college students to work as interns. You must be at least in your second semester of your senior year and be legal to work in the U.S. (at least 16).<br />
<br />
==== What is the minimum age to be an assistant in an Art of Problem Solving class? ====<br />
<br />
:You must have graduated from high school, or at least be in the second term of your senior year.<br />
<br />
== School ==<br />
<br />
==== What if I want to drop out of a class? ====<br />
:For any course with more than 2 classes, students can drop the course any time before the third class begins and receive a full refund. No drops are allowed after the third class has started. To drop the class, go to the My Classes section by clicking the My Classes link at the top-right of the website. Then find the area on the right side of the page that lets you drop the class. A refund will be processed within 10 business days.<br />
<br />
==== What if I miss a class? ====<br />
:There are classroom transcripts available under My Classes, available at the top right of the web site. You can view these transcripts in order to review any missed material. You can also ask questions on the class message board.<br />
<br />
==== Are there any audio and video during class? ====<br />
:There is no audio or video in the class. The classes are completely text based, in an interactive chat room environment, which allows students to ask questions at any time during the class. In addition to audio and video limiting interactivity, the technology isn't quite there yet for all students to be able to adequately receive streaming audio and video.<br />
<br />
==== I feel like joining! But what are my class choices? ====<br />
:[http://www.artofproblemsolving.com/School/classlist.php Class List] [http://www.artofproblemsolving.com/School/index.php?page=school.instructors Instructors List]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=43238User:Bluecarneal2011-11-24T15:42:22Z<p>Bluecarneal: /* Milestones */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (267)==<br />
===Problems Added but Didn't Post Myself (107)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1991&sid=85a6221e1d54bf1859580fb0643babba 1991 AHSME] (16-30)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
30,000th view (11/24/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42886User:Bluecarneal2011-11-02T03:09:42Z<p>Bluecarneal: /* RManaging (252) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (267)==<br />
===Problems Added but Didn't Post Myself (107)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1991&sid=85a6221e1d54bf1859580fb0643babba 1991 AHSME] (16-30)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42448User:Bluecarneal2011-10-02T19:14:30Z<p>Bluecarneal: /* RManaging (234) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (252)==<br />
===Problems Added but Didn't Post Myself (92)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42447User:Bluecarneal2011-10-02T16:21:58Z<p>Bluecarneal: /* RManaging (228) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (234)==<br />
===Problems Added but Didn't Post Myself (74)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-12)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=2007&sid=2144c150d9ffb86e37d9c779c1d27949 2007 Turkey NMO] (Days 1-2)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42439User:Bluecarneal2011-09-30T19:27:06Z<p>Bluecarneal: /* Problems Edited For Contest Page (64) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (228)==<br />
===Problems Added but Didn't Post Myself (68)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-12)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (71)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (1-6,10)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42438User:Bluecarneal2011-09-30T19:17:30Z<p>Bluecarneal: /* RManaging (222) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (228)==<br />
===Problems Added but Didn't Post Myself (68)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=44&year=1986 1986 AHSME] (6-9,11-12)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42424User:Bluecarneal2011-09-28T14:10:27Z<p>Bluecarneal: /* RManaging (216) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (222)==<br />
===Problems Added but Didn't Post Myself (62)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=96&year=1996 1996 Turkey TST] (Day 1-2)<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42423User:Bluecarneal2011-09-28T11:36:28Z<p>Bluecarneal: /* RManaging (210) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (216)==<br />
===Problems Added but Didn't Post Myself (56)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=174&cid=95&year=1997 1997 Turkey NMO] (Day 1-2)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42422User:Bluecarneal2011-09-28T11:32:02Z<p>Bluecarneal: /* Problems Added but Didn't Post Myself (44) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (210)==<br />
===Problems Added but Didn't Post Myself (50)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42421User:Bluecarneal2011-09-28T11:31:43Z<p>Bluecarneal: /* RManaging (204) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (210)==<br />
===Problems Added but Didn't Post Myself (44)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=217&year=2011&sid=40b7f9fa21661bd1a1bddca7c5500fea Lusophon MO 2011] (Day 1-2)<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42373User:Bluecarneal2011-09-20T20:21:19Z<p>Bluecarneal: /* 2008 AMC 8 (21) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/20/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (204)==<br />
===Problems Added but Didn't Post Myself (44)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42372User:Bluecarneal2011-09-20T20:21:07Z<p>Bluecarneal: /* AMC 10 Training (10th grade) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
===2008 AMC 8 (21)===<br />
(9/19/11) Don't take math tests in moving vehicles. Seriously. Ugh.<br />
<br />
==RManaging (204)==<br />
===Problems Added but Didn't Post Myself (44)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Contest_Statistics&diff=42369Contest Statistics2011-09-19T22:57:49Z<p>Bluecarneal: </p>
<hr />
<div>=AMC 8=<br />
===2010===<br />
Number of Student Participants: 153211<br />
<br />
Overall Average Score: 9.98<br />
<br />
Number of Perfect Scores: 499<br />
<br />
[http://amc.maa.org/amc8/2010/stats/GLOBALSTATS.HTML Source]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Contest_Statistics&diff=42368Contest Statistics2011-09-19T22:57:29Z<p>Bluecarneal: /* 2010 */</p>
<hr />
<div>=AMC 8=<br />
===2010===<br />
Number of Student Participants 153211<br />
<br />
Overall Average Score 9.98<br />
<br />
Number of Perfect Scores 499<br />
<br />
[http://amc.maa.org/amc8/2010/stats/GLOBALSTATS.HTML Source]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Contest_Statistics&diff=42367Contest Statistics2011-09-19T22:56:02Z<p>Bluecarneal: /* 1985 */</p>
<hr />
<div>=AMC 8=<br />
===2010===<br />
NUmber of Student Participants 153211<br />
<br />
Overall Average Score 9.98<br />
<br />
[http://amc.maa.org/amc8/2010/stats/GLOBALSTATS.HTML Source]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Contest_Statistics&diff=42366Contest Statistics2011-09-19T22:52:31Z<p>Bluecarneal: </p>
<hr />
<div>=AMC 8=<br />
===1985===</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Contest_Statistics&diff=42365Contest Statistics2011-09-19T22:51:43Z<p>Bluecarneal: </p>
<hr />
<div>=American Mathematics Competitions=<br />
==AMC 8==</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Contest_Statistics&diff=42364Contest Statistics2011-09-19T22:51:15Z<p>Bluecarneal: </p>
<hr />
<div>=American Mathematics Competitions=</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=Contest_Statistics&diff=42363Contest Statistics2011-09-19T22:51:06Z<p>Bluecarneal: Created page with "=American Mathematics Competitions"</p>
<hr />
<div>=American Mathematics Competitions</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42354User:Bluecarneal2011-09-19T17:19:30Z<p>Bluecarneal: /* AMC 10 Training (10th grade) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
===2001 AMC 10 (111)===<br />
(9/19/11) Looking good. With algebra review, Intermediate Algebra, and a skimming of Intro to C+P, I should be able to get 130+ consistently by spring.<br />
<br />
==RManaging (204)==<br />
===Problems Added but Didn't Post Myself (44)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarnealhttps://artofproblemsolving.com/wiki/index.php?title=User:Bluecarneal&diff=42351User:Bluecarneal2011-09-18T22:22:17Z<p>Bluecarneal: /* AMC 10 Training (10th grade) */</p>
<hr />
<div>===bluecarneal===<br />
This is an ongoing progress to interlink a database here with my blog description. If you read this, pm me with the number "963" to receive 10 BP.<br />
If you edit this page, please be aware that I will probably change it back to where it was before without warning, unless, of course, you did something that was useful.<br />
<br />
==AMC 10 Training (10th grade)==<br />
===1996 AMC 8 (21)===<br />
(8/19/11)<br />
The first one I took. I'm going to try to go through a few tests a week, variously AMC 8s and 10s. I'm aiming for qualification in the AIME, which means that I need a 120. Here I am starting out with AMC 8s. I got a 21 on this one. If I had read how they were scored, I would've approached the test a bit differently and got a 23. I made a stupid mistake on 6 (ouch), misread 8, and didn't approach 16 correctly. If I had guessed, though, I would've gotten it right. On 20 I used my awesome process of elimination skills and... eliminated the answer. I will not let myself move on to AMC 10's until I get a 25. (Maybe 2 of them, if it doesn't happen soon)<br />
===2001 AMC 8 (22)===<br />
(8/19/11) Bleh. I had to look up one of the problems because it wasn't complete, and I tried to do another of them without the diagram (which didn't exist). I missed 24 (being stupid), 20 (guessed the wrong one out of 2 possibles), and 14 (need to review Intro to C+P BADLY). Other than that, I need to remember I still have like 5 months left, Algebra 1 and 2 review for fun (AoPS Style) and Algebra 3. Throw in some C+P and I should be fine. I just can't let geo sneak up on me...<br />
===1988 AMC 8 (24)===<br />
(8/20/11) That's more like it. I would've had a 25 except for #16, where I basically did the opposite of the correct answer. Including instead of excluding the diagonal. I'm finding a lot of typos/errors, so I'll continue to do these for practice and for making them a better resource for the community.<br />
===2005 AMC 8 (20)===<br />
(8/20/11) Bleh. This seems to be one of the harder ones so far, and it hit me right in the geo and C+P. *sigh*<br />
===1990 AMC 8 (21)===<br />
(8/28/11) 9 was a fail. 12 was a fail. 16... I'm ok with missing that one, same with 19. Actually, this should've been 23. Grr. Need to check my work. <br />
===1993 AMC 8 (24)===<br />
I missed number 24. I noticed the "wrong" pattern. SO CLOSE.<br />
===2006 AMC 8 (25)===<br />
(8/29/11) YAY! Since it took me this long to get a perfect, I'll try for another before starting the AMC 10s. Then I'll sprinkle in an AMC 8 every 2 or 3 contests. (Not that I remembered the answers, but many of these problems... I remember them from FTW.<br />
===1995 AMC 8 (24)===<br />
(8/?/11) Missed #18. Found it on my desk ungraded from last month, so I don't remember much about it :P<br />
<br />
==RManaging (204)==<br />
===Problems Added but Didn't Post Myself (44)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2011 2011 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2008 2008 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=69&year=2009 2009 MMO] (1-4)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=80&cid=101&year=2011 INMO Round 3] (All [32])<br />
<br />
===Problems Posted by Me but not Added by Me (93)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=42&year=1997 1997 AJHSME] (1-25)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?mode=edit_problems&c=182&cid=38&year=2002 2002 USAMTS Rounds 3-4] (1-5,1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=1&cid=153&year=2001 2001 Tournament of Towns] (1-48)<br />
===Problems Posted and Added by Me (67)===<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2005 2005 USAMTS Round 4] (1-5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=166&year=2006&sid=caff6696bb901f1c974ef1b99399fcc0 2006 SMT {Team Round, Algebra Round}] ({2,4,6-15},{6-10})<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=38&year=2004&sid=8ec28cfe922d3c333a960c6015a7e60d 2004 USAMTS Rounds 2 and 4] (1-5),(1,5)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1966&sid=ed4ed60177087d054086c5b1cc8059b3 1966 AHSME] (27-40)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1968&sid=ed4ed60177087d054086c5b1cc8059b3 1968 AHSME] (1-20)<br />
<br />
===Problems Edited For Contest Page (64)===<br />
Note to self: Doesn't count toward total<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1950 1950 AHSME] (1-50)<br />
<br />
[http://www.artofproblemsolving.com/Forum/resources.php?c=182&cid=44&year=1995&sid=ed4ed60177087d054086c5b1cc8059b3 1995 AHSME] (17-30)<br />
<br />
==Milestones==<br />
100 views per day achieved (1/9/11)<br />
<br />
100 comments (1/7/11)<br />
<br />
1000th view (1/10/11)<br />
<br />
50th entry (1/10/11)<br />
<br />
200 comments (1/12/11)<br />
<br />
1337th view (1/12/11)<br />
<br />
1500th view:(1/14/11)<br />
<br />
300th comment (1/16/11)<br />
<br />
2000th view (1/17/11)<br />
<br />
2500th view (1/19/11)<br />
<br />
3000th view (1/23/11)<br />
<br />
4000th view (2/1/11)<br />
<br />
500th comment (2/3/11)<br />
<br />
5000th view (2/7/11)<br />
<br />
6000th view (2/16/11)<br />
<br />
200th entry (2/16/11)<br />
<br />
600th comment (2/17/11)<br />
<br />
40th update (2/21/11)<br />
<br />
7000th view (2/23/11)<br />
<br />
8000th view (2/28/11)<br />
<br />
700th comment (3/4/11)<br />
<br />
50th update (3/5/11)<br />
<br />
9000th view (3/7/11)<br />
<br />
10000th view (3/13/11)<br />
<br />
300th entry (3/14/11)<br />
<br />
15,000th view (4/11/11)<br />
<br />
400th entry (4/28/11)<br />
<br />
1,000th Comment (5/23/11)<br />
<br />
20,000th view (6/13/11)<br />
<br />
25,000th view (8/25/11)<br />
<br />
==Games I've Created==<br />
===Fun Factory===<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=319376&hilit=either+or Either Or]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538&start=0 Average Posts Per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=379609 Thermal Necropost]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=384475 You OXYMORON!]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=382803 The Username Game]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=376538 Average Posts per User]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=344457 The Awesome Geography Game (revival)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=304600 Time Travellers]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=289356 Count to 100,000]<br />
<br />
===Games===<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=382034&start=0 THE MAZE (Hosted by Blue)]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=387908 Reaper 2.0]<br />
<br />
[http://www.artofproblemsolving.com/Forum/viewtopic.php?f=535&t=409544 The Letter Market II]<br />
<br />
==Records I hold on AoPS==<br />
Longest Reverse Necropost "Post": [http://www.artofproblemsolving.com/Forum/viewtopic.php?p=2123991#p2123991 3 days, 12 hours, 23 minutes]<br />
<br />
Longest Necropost Game: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Longest Game with Defined End that Ended: [http://www.artofproblemsolving.com/Forum/viewtopic.php?f=139&t=321321&start=0 Necropost II]<br />
<br />
Most Reaps: [http://www.artofproblemsolving.com/Edutainment/Reaper/game.php?game_id=15 9500 (data lost)]<br />
<br />
Longest Reaper Lead: Game 18, between 5 and 6 months.<br />
<br />
===Personal Blog Records===<br />
200 views in 7 hours (1/17/11)<br />
<br />
2.94 shouts/day (1/17/11)<br />
<br />
4.36 comments/entry (1/21/11)<br />
<br />
257 line description (1/21/11)<br />
<br />
4.8 entries per day (1/20/11)<br />
<br />
152.12 views/day (4/2/11)<br />
<br />
42.42 views/entry (7/25/11)<br />
<br />
==Useful Tags==<br />
===Problem of the Day===<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Solved This is a complete list of all solved problems.] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day%20-%20Unsolved This is a complete list of all unsolved problems.]<br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Problem%20of%20the%20Day This is a complete list of all problems] <br />
<br />
[http://www.artofproblemsolving.com/Forum/blog.php?u=38516&tag=Special Problem of the Day Contributor Created Special Problems of the Day]</div>Bluecarneal