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Tech support and questions about AoPS classes and materials
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Site Support Tech support and questions about AoPS classes and materials
Tech support and questions about AoPS classes and materials
3 M G
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what number have you memorized perfect squares
ellenssim   18
N 2 hours ago by lavender_cloud
Up to what number have you memorized perfect squares, and how often does it help you in solving problems?
18 replies
ellenssim
May 28, 2025
lavender_cloud
2 hours ago
1234th Post!
PikaPika999   264
N 2 hours ago by PikaPika999
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
264 replies
PikaPika999
Apr 21, 2025
PikaPika999
2 hours ago
Find the amount of possible values from the expression
Darealzolt   2
N 2 hours ago by Elephant12
Find the amount of possible values from
\[
\frac{|a|}{a}+\frac{|b|}{b}+\frac{|c|}{c}
\]For all non zero integers \(a,b,c\)
2 replies
Darealzolt
Today at 4:15 AM
Elephant12
2 hours ago
Standard Factoring/Manipulation
Darealzolt   1
N 2 hours ago by Andyluo
Find the value of the following expression
\[
\frac{4000^2+4050^2}{(2000+2025)^2+(2000-2025)^2}
\]
1 reply
Darealzolt
2 hours ago
Andyluo
2 hours ago
Worst math problems
LXC007   7
N Today at 5:10 AM by buddyram
What is the most egregiously bad problem or solution you have encountered in school?
7 replies
LXC007
May 21, 2025
buddyram
Today at 5:10 AM
Challenge: Make every number to 100 using 4 fours
CJB19   267
N Today at 3:56 AM by Marshall_Huang
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:
$$(4-4)*4*4=0$$$$4-4+4/4=1$$$$4/4+4/4=2$$$$(4+4+4)/4=3$$$$4+(4-4)*4=4$$$$4+4^{4-4}=5$$$$4!/4+4-4=6$$$$4+4-4/4=7$$$$4+4+4-4=8$$
267 replies
CJB19
May 15, 2025
Marshall_Huang
Today at 3:56 AM
Trivial Factoring MathCounts Question? 2025 MathCounts National Sprint Round #29
ilikemath247365   35
N Today at 2:56 AM by Andyluo
What is the value of the expression below?

$\frac{(1! + 2! + 3!)(2! + 3! + 4!)(3! + 4! + 5!)...(98! + 99! + 100!)}{(1! - 3(2!) + 3!)(2! - 3(3!) + 4!)(3! - 3(4!) + 5!)...(98! - 3(99!) + 100!)}$.
35 replies
ilikemath247365
May 28, 2025
Andyluo
Today at 2:56 AM
The daily problem!
Leeoz   214
N Today at 1:51 AM by maxamc
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!
214 replies
Leeoz
Mar 21, 2025
maxamc
Today at 1:51 AM
Last challenge problems in the books
ysn613   18
N Today at 12:24 AM by valenbb
Algebra
It is known that $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}\dots=\frac{\pi^2}{6}$ Given this fact, determine the exact value of $$\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}\dots.$$(Source: Mandelbrot)
Counting and Probability
A $3\times3\times3$ wooden cube is painted on all six faces, then cut into 27 unit cubes. One unit cube is randomly selected and rolled. After it is rolled, $5$ out of the $6$ faces are visible. What is the probability that exactly one of the five visible faces is painted? (Source: MATHCOUNTS)
Number Theory(This technically isn't the last problem but the last chapter doesn't have challenge problems)
The integer p is a 50-digit prime number. When its square is divided by 120, the remainder is not 1. What is the remainder?
I didn't include geometry because I haven't taken it yet, feel free to post it
Answer these problems and post what you think is the order of difficulty
18 replies
ysn613
May 26, 2025
valenbb
Today at 12:24 AM
Math with Connect4 Boards
Math-lover1   8
N Today at 12:16 AM 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
8 replies
Math-lover1
May 1, 2025
Math-lover1
Today at 12:16 AM
a