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Contests & Programs AMC and other contests, summer programs, etc.
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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]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
May 1, 2025
0 replies
k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
Essentially, how to get good at olympiad math?
gulab_jamun   0
an hour ago
Ok, so I'm posting this as an anynonymous user cuz I don't want to get flamed by anyone I know for my goals but I really do want to improve on my math skill.

Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!
0 replies
+2 w
gulab_jamun
an hour ago
0 replies
9 best high school math competitions hosted by a college/university
ethan2011   15
N an hour ago by happypi31415
I only included college-hosted comps since MAA comps are very differently formatted, and IMO would easily beat the rest on quality since mathematicians around the world give questions, and so many problems are shortlisted, so IMO does release the IMO shortlist for people to practice. I also did not include the not as prestigious ones(like BRUMO, CUBRMC, and others), since most comps with very high quality questions are more prestigious(I did include other if you really think those questions are really good).
15 replies
1 viewing
ethan2011
Apr 12, 2025
happypi31415
an hour ago
Interesting inequalities
sqing   3
N an hour ago by sqing
Source: Own
Let $ a,b >0 $ and $ a^2-ab+b^2\leq 1 $ . Prove that
$$a^4 +b^4+\frac{a }{b +1}+ \frac{b }{a +1} \leq 3$$$$a^3 +b^3+\frac{a^2}{b^2+1}+ \frac{b^2}{a^2+1} \leq 3$$$$a^4 +b^4-\frac{a}{b+1}-\frac{b}{a+1} \leq 1$$$$a^4+b^4 -\frac{a^2}{b^2+1}- \frac{b^2}{a^2+1}\leq 1$$$$a^3+b^3 -\frac{a^3}{b^3+1}- \frac{b^3}{a^3+1}\leq 1$$
3 replies
sqing
May 9, 2025
sqing
an hour ago
Marking vertices in splitted triangle
mathisreal   2
N an hour ago by sopaconk
Source: Mexico
Let $n$ be a positive integer. Consider a figure of a equilateral triangle of side $n$ and splitted in $n^2$ small equilateral triangles of side $1$. One will mark some of the $1+2+\dots+(n+1)$ vertices of the small triangles, such that for every integer $k\geq 1$, there is not any trapezoid(trapezium), whose the sides are $(1,k,1,k+1)$, with all the vertices marked. Furthermore, there are no small triangle(side $1$) have your three vertices marked. Determine the greatest quantity of marked vertices.
2 replies
mathisreal
Feb 7, 2022
sopaconk
an hour ago
[TEST RELEASED] OMMC Year 5
DottedCaculator   72
N an hour ago by PikaPika999
Test portal: https://ommc-test-portal-2025.vercel.app/

Hello to all creative problem solvers,

Do you want to work on a fun, untimed team math competition with amazing questions by MOPpers and IMO & EGMO medalists? $\phantom{You lost the game.}$
Do you want to have a chance to win thousands in cash and raffle prizes (no matter your skill level)?

Check out the fifth annual iteration of the

Online Monmouth Math Competition!

Online Monmouth Math Competition, or OMMC, is a 501c3 accredited nonprofit organization managed by adults, college students, and high schoolers which aims to give talented high school and middle school students an exciting way to develop their skills in mathematics.

Our website: https://www.ommcofficial.org/
Our Discord (6000+ members): https://tinyurl.com/joinommc

This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read carefully and thoroughly. Join our Discord or monitor this thread for updates and test releases.

How hard is it?

We plan to raffle out a TON of prizes over all competitors regardless of performance. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!

How are the problems?

You can check out our past problems and sample problems here:
https://www.ommcofficial.org/sample
https://www.ommcofficial.org/2022-documents
https://www.ommcofficial.org/2023-documents
https://www.ommcofficial.org/ommc-amc

How will the test be held?/How do I sign up?

Solo teams?

Test Policy

Timeline:
Main Round: May 17th - May 24th
Test Portal Released. The Main Round of the contest is held. The Main Round consists of 25 questions that each have a numerical answer. Teams will have the entire time interval to work on the questions. They can submit any time during the interval. Teams are free to edit their submissions before the period ends, even after they submit.

Final Round: May 26th - May 28th
The top placing teams will qualify for this invitational round (5-10 questions). The final round consists of 5-10 proof questions. Teams again will have the entire time interval to work on these questions and can submit their proofs any time during this interval. Teams are free to edit their submissions before the period ends, even after they submit.

Conclusion of Competition: Early June
Solutions will be released, winners announced, and prizes sent out to winners.

Scoring:

Prizes:

I have more questions. Whom do I ask?

We hope for your participation, and good luck!

OMMC staff

OMMC’S 2025 EVENTS ARE SPONSORED BY:

[list]
[*]Nontrivial Fellowship
[*]Citadel
[*]SPARC
[*]Jane Street
[*]And counting!
[/list]
72 replies
+2 w
DottedCaculator
Apr 26, 2025
PikaPika999
an hour ago
distance of a point from incircle equals to a diameter of incircle
parmenides51   5
N an hour ago by Captainscrubz
Source: 2019 Oral Moscow Geometry Olympiad grades 8-9 p1
In the triangle $ABC, I$ is the center of the inscribed circle, point $M$ lies on the side of $BC$, with $\angle BIM = 90^o$. Prove that the distance from point $M$ to line $AB$ is equal to the diameter of the circle inscribed in triangle $ABC$
5 replies
parmenides51
May 21, 2019
Captainscrubz
an hour ago
No math to big math in 42 days
observer04   1
N an hour ago by c_double_sharp
CAN IT BE DONE





usajmo
1 reply
observer04
2 hours ago
c_double_sharp
an hour ago
f(a + b) = f(a) + f(b) + f(c) + f(d) in N-{O}, with 2ab = c^2 + d^2
parmenides51   8
N 5 hours ago by TiagoCavalcante
Source: RMM Shortlist 2016 A1
Determine all functions $f$ from the set of non-negative integers to itself such that $f(a + b) = f(a) + f(b) + f(c) + f(d)$, whenever $a, b, c, d$, are non-negative integers satisfying $2ab = c^2 + d^2$.
8 replies
parmenides51
Jul 4, 2019
TiagoCavalcante
5 hours ago
Functional Inequality Implies Uniform Sign
peace09   33
N 5 hours ago by ezpotd
Source: 2023 ISL A2
Let $\mathbb{R}$ be the set of real numbers. Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that \[f(x+y)f(x-y)\geqslant f(x)^2-f(y)^2\]for every $x,y\in\mathbb{R}$. Assume that the inequality is strict for some $x_0,y_0\in\mathbb{R}$.

Prove that either $f(x)\geqslant 0$ for every $x\in\mathbb{R}$ or $f(x)\leqslant 0$ for every $x\in\mathbb{R}$.
33 replies
peace09
Jul 17, 2024
ezpotd
5 hours ago
Labelling edges of Kn
oVlad   1
N 6 hours ago by TopGbulliedU
Source: Romania Junior TST 2025 Day 2 P3
Let $n\geqslant 3$ be an integer. Ion draws a regular $n$-gon and all its diagonals. On every diagonal and edge, Ion writes a positive integer, such that for any triangle formed with the vertices of the $n$-gon, one of the numbers on its edges is the sum of the two other numbers on its edges. Determine the smallest possible number of distinct values that Ion can write.
1 reply
oVlad
May 6, 2025
TopGbulliedU
6 hours ago
c^a + a = 2^b
Havu   8
N Yesterday at 8:29 PM by MathematicalArceus
Find $a, b, c\in\mathbb{Z}^+$ such that $a,b,c$ coprime, $a + b = 2c$ and $c^a + a = 2^b$.
8 replies
Havu
May 10, 2025
MathematicalArceus
Yesterday at 8:29 PM
Concurrence of lines defined by intersections of circles
Lukaluce   1
N Yesterday at 8:28 PM by sarjinius
Source: 2025 Macedonian Balkan Math Olympiad TST Problem 2
Let $\triangle ABC$ be an acute-angled triangle and $A_1, B_1$, and $C_1$ be the feet of the altitudes from $A, B$, and $C$, respectively. On the rays $AA_1, BB_1$, and $CC_1$, we have points $A_2, B_2$, and $C_2$ respectively, lying outside of $\triangle ABC$, such that
\[\frac{A_1A_2}{AA_1} = \frac{B_1B_2}{BB_1} = \frac{C_1C_2}{CC_1}.\]If the intersections of $B_1C_2$ and $B_2C_1$, $C_1A_2$ and $C_2A_1$, and $A_1B_2$ and $A_2B_1$ are $A', B'$, and $C'$ respectively, prove that $AA', BB'$, and $CC'$ have a common point.
1 reply
Lukaluce
Apr 14, 2025
sarjinius
Yesterday at 8:28 PM
Factorial Divisibility
Aryan-23   45
N Yesterday at 8:28 PM by MathematicalArceus
Source: IMO SL 2022 N2
Find all positive integers $n>2$ such that
$$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$
45 replies
Aryan-23
Jul 9, 2023
MathematicalArceus
Yesterday at 8:28 PM
Multiple of multinomial coefficient is an integer
orl   14
N Yesterday at 8:23 PM by mickeymouse7133
Source: Romanian Master in Mathematics 2009, Problem 1
For $ a_i \in \mathbb{Z}^ +$, $ i = 1, \ldots, k$, and $ n = \sum^k_{i = 1} a_i$, let $ d = \gcd(a_1, \ldots, a_k)$ denote the greatest common divisor of $ a_1, \ldots, a_k$.
Prove that $ \frac {d} {n} \cdot \frac {n!}{\prod\limits^k_{i = 1} (a_i!)}$ is an integer.

Dan Schwarz, Romania
14 replies
orl
Mar 7, 2009
mickeymouse7133
Yesterday at 8:23 PM
How to prepare for the USAMO/Making Red MOP
andrewma08   10
N Apr 14, 2011 by pythag011
Hey AOPSers,

I'm currently a sophomore, and this year is my second year in a row that I've made USAMO. I happen to suck at proofs. Alot.

Last year, I bombed the AMC 12 (100.5) and aced the AIME (11) to barely scrape by and get a 9 on USAMO = no Red MOP for me.

This year, I aced the AMC 12 (144) and semi-not failed the AIME I (10) and am studying hard to make MOP.


What materials would best prepare me to achieve MOP? Again, my proof-writing skills are sub-par. Will this be incredibly difficult?

I'm currently reading Problems from the Book and 103 Trig Problems because I happen to be weak at both theory and trig. Suggestions/comments?
10 replies
andrewma08
Apr 9, 2011
pythag011
Apr 14, 2011
How to prepare for the USAMO/Making Red MOP
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andrewma08
8 posts
#1 • 2 Y
Y by Adventure10, Mango247
Hey AOPSers,

I'm currently a sophomore, and this year is my second year in a row that I've made USAMO. I happen to suck at proofs. Alot.

Last year, I bombed the AMC 12 (100.5) and aced the AIME (11) to barely scrape by and get a 9 on USAMO = no Red MOP for me.

This year, I aced the AMC 12 (144) and semi-not failed the AIME I (10) and am studying hard to make MOP.


What materials would best prepare me to achieve MOP? Again, my proof-writing skills are sub-par. Will this be incredibly difficult?

I'm currently reading Problems from the Book and 103 Trig Problems because I happen to be weak at both theory and trig. Suggestions/comments?
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donutsupernova
423 posts
#2 • 1 Y
Y by Adventure10
If you're starting olympiad prep right now, I would recommend that you don't try and patch your weaknesses. There's no way you can get it up to olympiad level in one month, so you should focus on getting your strengths to olympiad level.
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not_trig
2049 posts
#3 • 4 Y
Y by Adventure10, Mango247, and 2 other users
You should have enough time to do all the USAMO 1/4s in recent history. Do them. Write them up and show them to someone who knows what they're doing.
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pythag011
2453 posts
#4 • 4 Y
Y by Adventure10, Mango247, and 2 other users
not_trig wrote:
You should have enough time to do all the USAMO 1/4s in recent history. Do them. Write them up and show them to someone who knows what they're doing.

PM me please with the solutions, I would actually love to do this, have a lot of spare time which I'm using pretty badly.
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benjamin7xx
294 posts
#5 • 2 Y
Y by Adventure10, Mango247
I have a simple question related to this: Which questions on the USAJMO are #1 and #4 on the USAMO? Are they #3 and #6 (on JMO)?
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NuncChaos
781 posts
#6 • 2 Y
Y by Adventure10, Mango247
In a word, yes.
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Differ
518 posts
#7 • 2 Y
Y by Adventure10, Mango247
pythag011 wrote:
have a lot of spare time which I'm using pretty badly.

By this you mean doing math problems, right?
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zephyredx
430 posts
#8 • 2 Y
Y by Adventure10, Mango247
pythag011 wrote:
not_trig wrote:
You should have enough time to do all the USAMO 1/4s in recent history. Do them. Write them up and show them to someone who knows what they're doing.

PM me please with the solutions, I would actually love to do this, have a lot of spare time which I'm using pretty badly.

This is a good idea. That way pythag011 can learn how to write proofs :P

Seconding the USAMO 1/4's idea. I did that for Red MOP two years ago and it really helped me gain confidence that I could get 2 full problems (provided nothing weird tripped me up...like a PARALLEL CASE *cough cough*) on the USAMO.
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pythag011
2453 posts
#9 • 1 Y
Y by Adventure10
Note:

ok, preferably when sending solutions to me write every single thought you have while solving the problem. Don't do this on actual tests, but doing this will let me analyze your weaknesses and strengths much better.

Basically, almost all who can't make red/green (or score enough to get on it) and at least 75% of people who do will have some HUGE gap that takes a second to fix and will improve their abillity greatly. It's significantly easier to find this gap if you send me solutions this way.
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VIPMaster
458 posts
#10 • 1 Y
Y by Adventure10
@pythag011: is this offer of pm-ing you our solutions for feedback available to everyone? if it is, i would really appreciate that.
Thank you.
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pythag011
2453 posts
#11 • 1 Y
Y by Adventure10
VIPMaster wrote:
@pythag011: is this offer of pm-ing you our solutions for feedback available to everyone? if it is, i would really appreciate that.
Thank you.

It's available for everyone. I'll be able to do it unless the number of people doing this exceeds 20 or so, which I can't see happening.

btw writing solutions for problems you DIDN"T solve, and the solution is your thoughts on the problem is often very useful.
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