[/quote]
,
.
be an even integer and let 
be real numbers satisfying 
.
such that 
,
,
,
be four points such that no three are collinear and 
.
,
,
be the orthocenters of 
,
,
,
,
,
are pairwise distinct and are concurrent. Show that the four points 
and 
be the circumcenter and orthocenter, respectively, of an acute scalene triangle 
intersects 
and 
at 
and 
respectively. Let 
denote the intersection of the circumcircles of triangles 
and 
other than 
and 
analogously by repeating this construction two more times. Prove that 
be a quadrilateral inscribed in a circle 
.
,
,
,
,
,
,
,
.
lies over 
.
table filled with natural numbers, we say it is a divisor table if:
-
,
-
,
for every 
.
is given. Determine the smallest natural number 
,
be integers so that the integers 
are divisible by 
be a fixed integer. There are 
beads on a circular necklace. You wish to paint the beads using 
consecutive beads every color appears at least once. Find the largest value of 
for which this task is 
possible.
!
candy bars. Let N & M be positive integers, what is N+M?
Y by dantx5, cerberus88, awesomeguy2, gaygaygaygay, nbute, jkyman, yrushi, zmyshatlp, DSL13, sachinpgupte, TsunamiStorm08, Adventure10, and 31 other users
Recently, many responses to threads have little or no explanation, with only an answer provided. These will not contribute to understanding and following the question and defeats the purpose of the math threads.
Here are some suggestions to improve the quality of your responses.
• If you are introducing a topic that would be unfamiliar to the general public of the forum, explain what it is and how it is applied to the specific problem.
• If you are using a non-standard approach to the problem, explain why it is a more efficient approach than the normal methods and algorithms, and elaborate upon why your method works in the particular case.
• If you are dealing with complex mathematical symbols, surround them with dollar signs ($$), and the website will automatically transfer the code to
. Learning codes is easy and makes examining a math question a lot easier. For example, one is definitely more likely to be satisfied by 
than 120=-x^5+3x^4+23x^3-27x^2-166x. Note that this is just a simple (polynomial) example, and the more complex notations would call for even more, like summation.
• When finished, judge your own solution, imagining if you didn't understand how to solve the problem whether you would have been helped by the solution or not. Although it may be hard to transfer your mind to the state of this hypothetical other person, it is a good skill to have and can really help improve the overall quality of forum posts.
• It is okay to state that you made a guess or carried out a dubious process, or to make a move that carries a mistake, as long as you point it out as a guess or an unsure solution. Mistakes are a defining characteristic of the human species, average thinkers and geniuses alike, so you should not be afraid to announce that you think you might have done something incorrectly in your solution—if you really don't know what the question is talking about though, don't answer it, as you would then be leading the unfortunate question-asker astray into an nonexistent dimension.
• Don't be afraid to use colors and graphics to explain. In fact, many people find that these make the solution much clearer as well as more interesting. External links to informational websites also help, but don't just post that link and call it a day for counting as your explanation; at least append a label describing the content on the other side of the link.
Of course, as with any set of rules, these are just standards and suggestions, and need not be strictly and dogmatically followed. When unsure, common sense is your best friend, and if you must defer beyond that, just follow the rules. Always keep in mind that the person reading your responses and explanations is most likely a high school ninth, tenth, or eleventh grader.
Here is an example of an excellent solution. The only improvement I would make to it is to explain exactly what it is a definition of. Note how the poster of that explanation showed an analogous case of committees to explain the situation that could possibly be confusing to some people, and that he even went above and beyond the standards by leaving a little for the original poster to solve for himself or herself, as well as hiding the solution in case a viewer wanted to try to solve the problem without accidentally looking at the solution. Note that it shows that you don't have to be an adult to be able to write good solutions. If you find a solution you particularly enjoyed or learned significantly from, rate it 5 or 6.
If you have spent the time to read this, thank you very much, and if you have given some thought as to how you compare to such standards, another thanks. As a last note, feel free to point out anything you notice or want to mention or suggest an alteration to the standards listed above. Moreover, questions are always welcome, and it is much better to first clarify something here than to have ruined a few threads because of a grave misunderstanding.
Here are some suggestions to improve the quality of your responses.
• If you are introducing a topic that would be unfamiliar to the general public of the forum, explain what it is and how it is applied to the specific problem.
• If you are using a non-standard approach to the problem, explain why it is a more efficient approach than the normal methods and algorithms, and elaborate upon why your method works in the particular case.
• If you are dealing with complex mathematical symbols, surround them with dollar signs ($$), and the website will automatically transfer the code to
. Learning codes is easy and makes examining a math question a lot easier. For example, one is definitely more likely to be satisfied by 
than 120=-x^5+3x^4+23x^3-27x^2-166x. Note that this is just a simple (polynomial) example, and the more complex notations would call for even more, like summation. • When finished, judge your own solution, imagining if you didn't understand how to solve the problem whether you would have been helped by the solution or not. Although it may be hard to transfer your mind to the state of this hypothetical other person, it is a good skill to have and can really help improve the overall quality of forum posts.
• It is okay to state that you made a guess or carried out a dubious process, or to make a move that carries a mistake, as long as you point it out as a guess or an unsure solution. Mistakes are a defining characteristic of the human species, average thinkers and geniuses alike, so you should not be afraid to announce that you think you might have done something incorrectly in your solution—if you really don't know what the question is talking about though, don't answer it, as you would then be leading the unfortunate question-asker astray into an nonexistent dimension.
• Don't be afraid to use colors and graphics to explain. In fact, many people find that these make the solution much clearer as well as more interesting. External links to informational websites also help, but don't just post that link and call it a day for counting as your explanation; at least append a label describing the content on the other side of the link.
Of course, as with any set of rules, these are just standards and suggestions, and need not be strictly and dogmatically followed. When unsure, common sense is your best friend, and if you must defer beyond that, just follow the rules. Always keep in mind that the person reading your responses and explanations is most likely a high school ninth, tenth, or eleventh grader.
Here is an example of an excellent solution. The only improvement I would make to it is to explain exactly what it is a definition of. Note how the poster of that explanation showed an analogous case of committees to explain the situation that could possibly be confusing to some people, and that he even went above and beyond the standards by leaving a little for the original poster to solve for himself or herself, as well as hiding the solution in case a viewer wanted to try to solve the problem without accidentally looking at the solution. Note that it shows that you don't have to be an adult to be able to write good solutions. If you find a solution you particularly enjoyed or learned significantly from, rate it 5 or 6.
If you have spent the time to read this, thank you very much, and if you have given some thought as to how you compare to such standards, another thanks. As a last note, feel free to point out anything you notice or want to mention or suggest an alteration to the standards listed above. Moreover, questions are always welcome, and it is much better to first clarify something here than to have ruined a few threads because of a grave misunderstanding.
This post has been edited 3 times. Last edited by phiReKaLk6781, Mar 28, 2010, 10:55 PM
"
