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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
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When to look at solutions - pre calc
omerrob13   1
N 29 minutes ago by abartoha
Hey all.
I am doing the precalc book, and unfortunately, im getting into the habit of looking in the solutions quite fast on a problem I did not able to make any progress on.
My goal is mainly to develop problem solving and reasonning skills.

I divide the problems in AOPS to 2:

- Challenge problems at the end of the of each chapter.
- The problems that teach you the material itself, and the problems at the end of each section (1.1,1.2, etc...)

For non challenging problems, It takes around 20 mins of me not be able to solve a problem, and look at the solutions for it

Is it too little?
My goal is mainly to develop problem solving and reasoning skills.
I'm not sure if it's too little time to bring to a regular problem, or its ok to give 20 mins to a problem and continue if making no progress.
1 reply
omerrob13
2 hours ago
abartoha
29 minutes ago
J
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an algebra problem
Asyrafr09   1
N 38 minutes ago by abartoha
Determine all real number($x,y,z$) that satisfy
$$x=1+\sqrt{y-z^2}$$$$y=1+\sqrt{z-x^2}$$$$z=1+\sqrt{x-y^2}$$
1 reply
Asyrafr09
an hour ago
abartoha
38 minutes ago
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f_n(x)=\sum sin(nx)/n
Urumqi   4
N 2 hours ago by Urumqi
$F_n(x)=\sum_{k=1}^{n}\frac{\sin (kx)}{k}$, prove that for all $x \in (0,\pi), F_n(x)>0$.

Thanks.
4 replies
Urumqi
Today at 2:13 AM
Urumqi
2 hours ago
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A Collection of Good Problems from my end
SomeonecoolLovesMaths   2
N 3 hours ago by SomeonecoolLovesMaths
This is a collection of good problems and my respective attempts to solve them. I would like to encourage everyone to post their solutions to these problems, if any. This will not only help others verify theirs but also perhaps bring forward a different approach to the problem. I will constantly try to update the pool of questions.

The difficulty level of these questions vary from AMC 10 to AIME. (Although the main pool of questions were prepared as a mock test for IOQM over the years)

Problem 1

Problem 2

Problem 3
2 replies
SomeonecoolLovesMaths
3 hours ago
SomeonecoolLovesMaths
3 hours ago
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No more topics!
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Easy Problem
MathleteMystic   2
N Apr 3, 2025 by Mathematicalprodigy37
Prove that among n integers we can always choose some of them whose sum is a multiple on n.

I do have a solution to this, but could someone write a more descriptive one, please? Something like the logic behind it...
2 replies
MathleteMystic
Apr 3, 2025
Mathematicalprodigy37
Apr 3, 2025
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Easy Problem
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Reveal topic tags
combinatorics
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MathleteMystic
7 posts
MathleteMystic
#1 h  Apr 3, 2025, 1:20 PM
Y by
Prove that among n integers we can always choose some of them whose sum is a multiple on n.

I do have a solution to this, but could someone write a more descriptive one, please? Something like the logic behind it...
Z K Y
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Sadigly
159 posts
Sadigly
#2 h  Apr 3, 2025, 1:35 PM
Y by
Consider $a_1;a_1+a_2;a_1+a_2+a_3;...;a_1+a_2+a_3+...+a_n$
Z K Y
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Mathematicalprodigy37
19 posts
Mathematicalprodigy37
#3 h  Apr 3, 2025, 3:05 PM • 1 Y
Y by MathleteMystic
Completing the above proof,
Consider a_1, a_2, a_1+a_2,...a_1+a_2+a_3+...+a_n. Notice this is a list of n+1 positive integers. Notice that, by the pigeonhole principle, then at least one of the first n positive integers must share a remainder modulo n with a_1+a_2+...+a_n. Then, take that number and subtract it from a_1+a_2+...+a_n. however, notice that this can be written as a sum of some a_i's! But we assumed that those 2 numbers have the same remainder when divided by n, so thus that number is not only can be written as a sum of some of a_i's, it is divisible by n. Thus we are done.
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