Stay ahead of learning milestones! Enroll in a class over the summer!

Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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Contests & Programs AMC and other contests, summer programs, etc.
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
Difficult combinatorics problem
shactal   1
N 21 minutes ago by shactal
Can someone help me with this problem? Let $n\in \mathbb N^*$. We call a distribution the act of distributing the integers from $1$
to $n^2$ represented by tokens to players $A_1$ to $A_n$ so that they all have the same number of tokens in their urns.
We say that $A_i$ beats $A_j$ when, when $A_i$ and $A_j$ each draw a token from their urn, $A_i$ has a strictly greater chance of drawing a larger number than $A_j$. We then denote $A_i>A_j$. A distribution is said to be chicken-fox-viper when $A_1>A_2>\ldots>A_n>A_1$ What is $R(n)$
, the number of chicken-fox-viper distributions?
1 reply
+1 w
shactal
4 hours ago
shactal
21 minutes ago
IMO Shortlist 2013, Number Theory #3
lyukhson   48
N 28 minutes ago by Ihatecombin
Source: IMO Shortlist 2013, Number Theory #3
Prove that there exist infinitely many positive integers $n$ such that the largest prime divisor of $n^4 + n^2 + 1$ is equal to the largest prime divisor of $(n+1)^4 + (n+1)^2 +1$.
48 replies
lyukhson
Jul 10, 2014
Ihatecombin
28 minutes ago
Interesting inequalities
sqing   5
N 32 minutes ago by sqing
Source: Own
Let $a,b,c \geq 0 $ and $ab+bc+ca- abc =3.$ Show that
$$a+k(b+c)\geq 2\sqrt{3 k}$$Where $ k\geq 1. $
Let $a,b,c \geq 0 $ and $2(ab+bc+ca)- abc =31.$ Show that
$$a+k(b+c)\geq \sqrt{62k}$$Where $ k\geq 1. $
5 replies
sqing
May 16, 2025
sqing
32 minutes ago
Find all functions $f$: \(\mathbb{R}\) \(\rightarrow\) \(\mathbb{R}\) such : $f(
guramuta   0
32 minutes ago
Find all functions $f$: \(\mathbb{R}\) \(\rightarrow\) \(\mathbb{R}\) such :
$f(x+yf(x)) + f(xf(y)-y) = f(x) - f(y) + 2xy$
0 replies
guramuta
32 minutes ago
0 replies
Mary and Pat play a number game, smallest initial integer for Pat not winning
parmenides51   4
N 34 minutes ago by LeYohan
Source: Irmo 2018 p1 q1
Mary and Pat play the following number game. Mary picks an initial integer greater than $2017$. She then multiplies this number by $2017$ and adds $2$ to the result. Pat will add $2019$ to this new number and it will again be Mary’s turn. Both players will continue to take alternating turns. Mary will always multiply the current number by $2017$ and add $2$ to the result when it is her turn. Pat will always add $2019$ to the current number when it is his turn. Pat wins if any of the numbers obtained by either player is divisible by $2018$. Mary wants to prevent Pat from winning the game.
Determine, with proof, the smallest initial integer Mary could choose in order to achieve this.
4 replies
parmenides51
Sep 16, 2018
LeYohan
34 minutes ago
d1-d2 divides n for all divisors d1, d2
a_507_bc   6
N an hour ago by Assassino9931
Source: Romania 3rd JBMO TST 2023 P1
Determine all natural numbers $n \geq 2$ with at most four natural divisors, which have the property that for any two distinct proper divisors $d_1$ and $d_2$ of $n$, the positive integer $d_1-d_2$ divides $n$.
6 replies
a_507_bc
May 20, 2023
Assassino9931
an hour ago
Good divisors and special numbers.
Nuran2010   4
N an hour ago by Assassino9931
Source: Azerbaijan Al-Khwarizmi IJMO TST 2024
$N$ is a positive integer. Call all positive divisors of $N$ which are different from $1$ and $N$ beautiful divisors.We call $N$ a special number when it has at least $2$ beautiful divisors and difference of any $2$ beautiful divisors divides $N$ as well. Find all special numbers.
4 replies
Nuran2010
Apr 29, 2025
Assassino9931
an hour ago
No math to big math in 42 days
observer04   3
N an hour ago by maxamc
CAN IT BE DONE





usajmo
3 replies
observer04
Today at 1:08 AM
maxamc
an hour ago
JBMO Shortlist 2023 N2
Orestis_Lignos   5
N an hour ago by Just1
Source: JBMO Shortlist 2023, N2
A positive integer is called Tiranian if it can be written as $x^2+6xy+y^2$, where $x$ and $y$ are (not necessarily distinct) positive integers. The integer $36^{2023}$ is written as the sum of $k$ Tiranian integers. What is the smallest possible value of $k$?

Proposed by Miroslav Marinov, Bulgaria
5 replies
Orestis_Lignos
Jun 28, 2024
Just1
an hour ago
Inequality on non-nagative numbers
TUAN2k8   3
N an hour ago by sqing
Source: My book
Let $a,b,c$ be non-nagative real numbers such that $a+b+c=3$.
Prove that $ab+bc+ca-abc \leq \frac{9}{4}$.
3 replies
TUAN2k8
2 hours ago
sqing
an hour ago
2-var inequality
sqing   2
N an hour ago by sqing
Source: Own
Let $ a,b>0,  ab^2+a+2b\geq4  $. Prove that$$  \frac{a}{2a+b^2}+\frac{2}{a+2}\leq 1$$
2 replies
sqing
Today at 6:16 AM
sqing
an hour ago
[TEST RELEASED] OMMC Year 5
DottedCaculator   73
N Today at 5:31 AM by Ruegerbyrd
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]
73 replies
+1 w
DottedCaculator
Apr 26, 2025
Ruegerbyrd
Today at 5:31 AM
Essentially, how to get good at olympiad math?
gulab_jamun   1
N Today at 5:12 AM by Konigsberg
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!
1 reply
gulab_jamun
Today at 1:53 AM
Konigsberg
Today at 5:12 AM
9 best high school math competitions hosted by a college/university
ethan2011   16
N Today at 4:23 AM by aarush.rachak11
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).
16 replies
ethan2011
Apr 12, 2025
aarush.rachak11
Today at 4:23 AM
Olympiad Problems Correlation with Computational?
FuturePanda   8
N Apr 30, 2025 by deduck
Hi everyone,

Recently I;ve started doing a lot of nice combo/algebra Olympiad problems(JMO, PAGMO, CMO, etc.) and I’ve got to say, it’s been pretty fun(I’m enjoying it!). I was wondering if doing Olympiad problems also helps increase computational abilities slightly. Currently I am doing 75% computational, 25% oly but if anyone has any expreience I want to switch it to 25% computational and 75% Olympiad, though I still want to have computational skills for ARML, AIME, SMT, BMT, HMMT, etc.

If anyone has any experience, please let me know!

Thank you so much in advance!
8 replies
FuturePanda
Apr 26, 2025
deduck
Apr 30, 2025
Olympiad Problems Correlation with Computational?
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FuturePanda
244 posts
#1
Y by
Hi everyone,

Recently I;ve started doing a lot of nice combo/algebra Olympiad problems(JMO, PAGMO, CMO, etc.) and I’ve got to say, it’s been pretty fun(I’m enjoying it!). I was wondering if doing Olympiad problems also helps increase computational abilities slightly. Currently I am doing 75% computational, 25% oly but if anyone has any expreience I want to switch it to 25% computational and 75% Olympiad, though I still want to have computational skills for ARML, AIME, SMT, BMT, HMMT, etc.

If anyone has any experience, please let me know!

Thank you so much in advance!
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jellybeanzzz
498 posts
#2 • 1 Y
Y by elasticwealth
Do the math you like doing, you’ll be much more productive. Just do enough computational to not lose your speed.
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Konigsberg
2235 posts
#3
Y by
Proof-oriented and computational contests share a broad difficulty overlap. For training, the real priority is simply to work on problems that are just beyond your current comfort zone—regardless of category.

In the difficulty “ladder” I created for my country's national system (later adapted for an international audience), the proof and computational tracks intersect mainly at two of the eleven tiers, C1 and C2, with a few proof contests also appearing in tiers B1–B2. You can find the full guide here: https://tinyurl.com/ContestGuideIntl
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FuturePanda
244 posts
#4 • 1 Y
Y by alextheadventurer
Thank you so much! I will definitely look into these resources.
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v_Enhance
6877 posts
#5 • 4 Y
Y by Alex-131, MathCosine, lord_of_the_rook, NicoN9
Currently I am doing 75% computational, 25% oly but if anyone has any expreience I want to switch it to 25% computational and 75% Olympiad
I would also support making this switch. From the problem-writing side, once students are proof-capable, I think it is just much easier to design instructive problems in Olympiad style than in short-answer style. So broadly speaking I think making this switch would help increase the quality of your study --- especially since it sounds like you're having fun, which means the problems are serving you well.
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jb2015007
1963 posts
#6
Y by
v_Enhance wrote:
Currently I am doing 75% computational, 25% oly but if anyone has any expreience I want to switch it to 25% computational and 75% Olympiad
I would also support making this switch. From the problem-writing side, once students are proof-capable, I think it is just much easier to design instructive problems in Olympiad style than in short-answer style. So broadly speaking I think making this switch would help increase the quality of your study --- especially since it sounds like you're having fun, which means the problems are serving you well.

orz
i also agree with this btw
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megarnie
5610 posts
#7
Y by
yeah you should do the switch it's definitely more fun but make sure you at least still practice your weaker spots (and everything in general) in computational and don't fail AIME in 10th grade like me

i didn't do enough computational practice the past year (especially in geo, which is my weakest subject) so I ended up not making oly this year
This post has been edited 4 times. Last edited by megarnie, Apr 30, 2025, 2:52 AM
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FuturePanda
244 posts
#8
Y by
v_Enhance wrote:
Currently I am doing 75% computational, 25% oly but if anyone has any expreience I want to switch it to 25% computational and 75% Olympiad
I would also support making this switch. From the problem-writing side, once students are proof-capable, I think it is just much easier to design instructive problems in Olympiad style than in short-answer style. So broadly speaking I think making this switch would help increase the quality of your study --- especially since it sounds like you're having fun, which means the problems are serving you well.

Thank you so much!
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deduck
238 posts
#9
Y by
no way konigsberg the goat replied

i remeber playing ftw with u a long time ago and i think lost XD
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