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SOLVE: CDR style problem quick algebra
ryfighter 3
N
5 hours ago
by cheltstudent
It takes 3 people 10 minutes to mow 2 lawns. How many minutes will it take for 2 people to mow 10 lawns? Express your answer in hours as a decimal.














3 replies
Math with Connect4 Boards
Math-lover1 12
N
5 hours ago
by Math-lover1
Hi! So I was playing Connect4 with my friends the other day and I wondered: how many "legal" arrangements of Connect4 can be reached at the ending position?
We assume that we do not stop the game when there is a four in a row, and we have 21 red pieces and 21 yellow pieces. We also drop the pieces one by one into a standard 7 by 6 board. We can start the game with any color piece.
https://en.wikipedia.org/wiki/Connect_Four
Initial Thoughts
Attempt to use one-to-one correspondences
We assume that we do not stop the game when there is a four in a row, and we have 21 red pieces and 21 yellow pieces. We also drop the pieces one by one into a standard 7 by 6 board. We can start the game with any color piece.
https://en.wikipedia.org/wiki/Connect_Four
Initial Thoughts
This problem seems easy at first; the number of arrangments is simply
However, I quickly saw that some boards

OOOOOOO
OOOOOOO
OOOOOOO
OOOOOOO
OOOOOOO
OOOOOOO
were impossible to construct by just dropping pieces one by one like a normal game.OOOOOOO
OOOOOOO
OOOOOOO
OOOOOOO
OOOOOOO
Attempt to use one-to-one correspondences
After I realized that my Initial Thoughts weren't going to work, I tried to use one-to-one correspondences. I represented the columns as ABCDEFG from left to right and represented dropping the red/yellow pieces as a string of length 21 of these letters. This seemed to solve my problem, but new roadblocks popped up.
Roadblock 1 There is more than one way to represent a certain configuration using this correspondence. A quick example
Roadblock 2 Even if we didn't overcount, we still need to account for the fact that the total number of A, B, C... over both of the strings have to each equal 7. The amount of cases (1 A goes to the red pieces, 6 As go to the yellow pieces,...) would be very difficult to calculate, even using a computer.
Roadblock 1 There is more than one way to represent a certain configuration using this correspondence. A quick example
red pieces fill all the left 3 columns, yellow pieces fill all the right 3 columns
shows that we overcount some configurations by using this method.Roadblock 2 Even if we didn't overcount, we still need to account for the fact that the total number of A, B, C... over both of the strings have to each equal 7. The amount of cases (1 A goes to the red pieces, 6 As go to the yellow pieces,...) would be very difficult to calculate, even using a computer.
12 replies
Challenge: Make every number to 100 using 4 fours
CJB19 272
N
5 hours ago
by bbojy
I've seen this attempted a lot but I want to see if the AoPS community can actually do it. Using ONLY 4 fours and math operations, make as many numbers as you can. Try to go in order. I'll start:

















272 replies
The daily problem!
Leeoz 216
N
Today at 1:42 PM
by kjhgyuio
Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)
Please hide solutions and answers, hints are fine though! :)
Problems usually get harder throughout the week, so Sunday is the easiest and Saturday is the hardest!
Past Problems!
Please hide solutions and answers, hints are fine though! :)
Problems usually get harder throughout the week, so Sunday is the easiest and Saturday is the hardest!
Past Problems!
[quote=March 21st Problem]Alice flips a fair coin until she gets 2 heads in a row, or a tail and then a head. What is the probability that she stopped after 2 heads in a row? Express your answer as a common fraction.[/quote]
Answer
[quote=March 22nd Problem]In a best out of 5 math tournament, 2 teams compete to solve math problems, with each of the teams having a 50% chance of winning each round. The tournament ends when one team wins 3 rounds. What is the probability that the tournament will end before the fifth round? Express your answer as a common fraction.[/quote]
Answer
[quote=March 23rd Problem]The equations of
and
intersect at the point
. What is the value of
?[/quote]
Answer
[quote=March 24th Problem]Anthony rolls two fair six sided dice. What is the sum of all the different possible products of his rolls?[/quote]
Answer
[quote=March 25th Problem]If
, find the value of
.[/quote]
Answer
[quote=March 26th Problem]There is a group of 6 friends standing in line. However, 3 of them don't want to stand next to each other. In how many ways can they stand in line?[/quote]
Answer
[quote=March 27th Problem]Two real numbers,
and
are chosen from 0 to 1. What is the probability that their positive difference is more than
?[/quote]
Answer
[quote=March 28th Problem]What is the least possible value of the expression
?[/quote]
Answer
[quote=March 29th Problem]How many integers from 1 to 2025, inclusive, contain the digit “1”?[/quote]
Answer
[quote=April 3rd Problem]In
families, there are
children respectively. If a random child from any of the families is chosen, what is the probability that the child has
siblings? Express your answer as a common fraction.[/quote]
Answer
[quote=April 5th Problem]A circle with a radius of 3 units is centered at the point (0,0) on the coordinate plane. How many lattice points, points which both of the coordinates are integers, are strictly inside the circle?[/quote]
Answer
[quote=April 6th Problem]If the probability that someone asks for a problem is
, find the probability that out of
people, exactly
of them ask for a problem.[/quote]
Answer
[quote=April 8th Problem]Find the value of
such that
.[/quote]
Answer
[quote=April 9th Problem]In unit square
, point
lies on diagonal
such that
. Find the area of quadrilateral
.[/quote]
Answer
[quote=April 10th Problem]An function in the form
has
,
, and
. Find the value of
.[/quote]
Answer
Answer

[quote=March 22nd Problem]In a best out of 5 math tournament, 2 teams compete to solve math problems, with each of the teams having a 50% chance of winning each round. The tournament ends when one team wins 3 rounds. What is the probability that the tournament will end before the fifth round? Express your answer as a common fraction.[/quote]
Answer

[quote=March 23rd Problem]The equations of




Answer

[quote=March 24th Problem]Anthony rolls two fair six sided dice. What is the sum of all the different possible products of his rolls?[/quote]
Answer

[quote=March 25th Problem]If


Answer

[quote=March 26th Problem]There is a group of 6 friends standing in line. However, 3 of them don't want to stand next to each other. In how many ways can they stand in line?[/quote]
Answer

[quote=March 27th Problem]Two real numbers,



Answer

[quote=March 28th Problem]What is the least possible value of the expression

Answer

[quote=March 29th Problem]How many integers from 1 to 2025, inclusive, contain the digit “1”?[/quote]
Answer

[quote=April 3rd Problem]In



Answer

[quote=April 5th Problem]A circle with a radius of 3 units is centered at the point (0,0) on the coordinate plane. How many lattice points, points which both of the coordinates are integers, are strictly inside the circle?[/quote]
Answer

[quote=April 6th Problem]If the probability that someone asks for a problem is



Answer

[quote=April 8th Problem]Find the value of


Answer

[quote=April 9th Problem]In unit square





Answer

[quote=April 10th Problem]An function in the form





Answer

216 replies
Overly wordy problems
ZMB038 11
N
Today at 5:48 AM
by Yiyj
Hey everyone, here we can post questions with way to many extraneous words, that are actually easy.
Try to solve the one above yours.
I'll start:
Click to reveal hidden text
Try to solve the one above yours.
I'll start:
Click to reveal hidden text
Maya's parents Kim and Richard invented chocolate bars. Each chocolate bar was 1 dollar. They then became billionaires by scamming children. Maya was 8 years old when she found out she can't get sick from eating too many chocolate bars. Richard decided to make a deal with Maya. For every 4 chocolate bars she ate Maya could exchange the wrappers for another candy bar. Maya spent money on the lottery, and somehow won
! If she spends
dollars on her parents chocolate bars, she can eat
candy bars. Let N & M be positive integers, what is N+M?



11 replies
Find the amount of possible values from the expression
Darealzolt 3
N
Today at 3:16 AM
by Justbrick
Find the amount of possible values from
For all non zero integers
![\[
\frac{|a|}{a}+\frac{|b|}{b}+\frac{|c|}{c}
\]](http://latex.artofproblemsolving.com/8/4/a/84a1a990f8bbde7670e9154dd9a46bb18c14d547.png)

3 replies
Area of Polygon
AIME15 54
N
Today at 2:44 AM
by CJB19
The area of polygon
, in square units, is
IMAGE

IMAGE
![\[ \textbf{(A)}\ 24 \qquad
\textbf{(B)}\ 30 \qquad
\textbf{(C)}\ 46 \qquad
\textbf{(D)}\ 66 \qquad
\textbf{(E)}\ 74
\]](http://latex.artofproblemsolving.com/8/2/f/82ffc15072ca99f6cd1abc312781eb4827817356.png)
54 replies
2500th Post!
PikaPika999 21
N
Today at 2:13 AM
by PikaPika999
I may be a bit late for this, but this is my 2500th post :)
Also this is going to be my last one until another big milestone bc I don't wanna clog up the MSM forum with my milestones
Also, since my 1000th post math story was locked due to a flamewar, here is my math story with a few updates :)
(This was also scripted so if there are any problems in my story, um... well, it is what it is)
Script starts:
When I had less than 25 posts on AoPS, I saw many people create threads about them getting 1000th posts and their math story. I thought I would never hit 1000 posts, but I did, and that thread got locked...
So, lol
Daycare
Preschool
Kindergarten
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
Sixth Grade
In conclusion, AoPS has helped me improve my math. Minor side note, but
Finally, I would like to say thank you to all the new friends I made and all the instructors on AoPS that taught me!
Another minor side note, but
and here are some problems ig :)
Problems
hopefully these problems weren't too easy lol
Also this is going to be my last one until another big milestone bc I don't wanna clog up the MSM forum with my milestones
Also, since my 1000th post math story was locked due to a flamewar, here is my math story with a few updates :)
(This was also scripted so if there are any problems in my story, um... well, it is what it is)
Script starts:
When I had less than 25 posts on AoPS, I saw many people create threads about them getting 1000th posts and their math story. I thought I would never hit 1000 posts, but I did, and that thread got locked...
because of this flamewar...
Pleasewhatever you do, don’t get this locked.
So, lol
I’ve been waiting for this *redemption* time for a long time, but
here we are, writing my math story againI may or may not be copying this from my 1000th post thread…
:)Daycare
I figured out I loved math when I was in daycare at the age of around 4. At the end of the “school year,” I was already skip counting by 9s until 90!
Preschool
Ngl, during my one year at preschool, my math level probably got worse.
Kindergarten
My practice of skip-counting from daycare was paying off. We were doing this activity where we counted items in rows and columns, but I could just multiply as a shortcut. I also started grinding Beast Academy
Which at the time didn’t have Level 1
First Grade
I finished all of Beast Academy, including Level 5. :bruce: Then, I started grinding khanacademy.
Second Grade
I learned how to multiply and divide fractions on khanacademy. Other than this, my second grade year was insignificant.
Third Grade
Same as preschool, ngl, during this year, my math level prolly got worse.
Fourth Grade
I started doing AoPS. I started off with Prealgebra, which was actually super easy overall
This is not encouraging skipping this lesson, you should still take this class.
This was also the year that I started to hate graphing...Fifth Grade
This year, I took both the Introduction to Algebra class and the Introduction to Geometry class!!
Well this one took my fifth to sixth grade summer...
Sixth Grade
I started taking the Intermediate Algebra course on AoPS, but at around week 14, my dad thought that I wasn’t ready for this class, so he enrolled me in the Introduction to Counting and Probability self-paced class. This class is really helpful to me because for some reason, around three-fifths of the problems in most competitions are from Counting and Probability if not more, and Counting and Probability was probably tied as my weakest subject with Number Theory
Can’t wait for Introduction to Number Theory’s self paced class comes out :)
In conclusion, AoPS has helped me improve my math. Minor side note, but
I have also made many new friends on AoPS!
Finally, I would like to say thank you to all the new friends I made and all the instructors on AoPS that taught me!
Another minor side note, but
Sorry if this was uninteresting or a complete waste of your time. Lolz :evilgrin:
and here are some problems ig :)
Problems
1. How many ways can you arrange the letters in the word ALGEBRA such that no two identical letters are adjacent?
2. Find the smallest positive integer n such that
is not a prime number.
3. You have 4 red tiles, 3 blue tiles, and 2 green tiles. How many ways can you arrange them in a row such that no two tiles of the same color are adjacent?
4. You flip a fair coin repeatedly until you either get 3 tails or 4 heads. What is the expected value of the number of flips before stopping?
5. Let
and
be two points in the coordinate plane. A circle is drawn such that
is a diameter.
(a). Find the equation of the circle in the form
(b). The are two tangents to the circle that pass through the point
. Find the equation of these lines.
2. Find the smallest positive integer n such that

3. You have 4 red tiles, 3 blue tiles, and 2 green tiles. How many ways can you arrange them in a row such that no two tiles of the same color are adjacent?
4. You flip a fair coin repeatedly until you either get 3 tails or 4 heads. What is the expected value of the number of flips before stopping?
5. Let



(a). Find the equation of the circle in the form

(b). The are two tangents to the circle that pass through the point

hopefully these problems weren't too easy lol
21 replies
9 Favorite topic
A7456321 33
N
Today at 1:45 AM
by A7456321
What is your favorite math topic/subject?
If you don't know why you are here, go binge watch something!
If you forgot why you are here, go to a hospital! :)
If you know why you are here and have voted, maybe say why you picked the option that you picked in a response) :thumbup:
if ur here for any reason whatsoever, CLICK ME YOU KNOW YOU WANT TO
Timeline
If you don't know why you are here, go binge watch something!
If you forgot why you are here, go to a hospital! :)
If you know why you are here and have voted, maybe say why you picked the option that you picked in a response) :thumbup:
if ur here for any reason whatsoever, CLICK ME YOU KNOW YOU WANT TO
ONCE YOU SEE THIS YOU MUST OBEY THE COMMAND WITHIN
upvote pls! :3 (._.)
Timeline
First vote! --- May 23, 2025
50 votes! --- May 24, 2025
100 votes! --- May 27, 2025
help me add more! :)
50 votes! --- May 24, 2025
100 votes! --- May 27, 2025
help me add more! :)
33 replies
