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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.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
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Thursday, Jun 12 - Sep 11

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MATHCOUNTS/AMC 8 Basics
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Thursday, May 22 - Jul 31

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F=ma Problem Series
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WOOT Programs
Visit the pages linked for full schedule details for each of these programs!


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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
OTIS or MathWOOT 2
math_on_top   6
N 11 minutes ago by MathCosine
Hey AoPS community I took MathWOOT 1 this year and scored an 8 on AIME (last year I got a 6). My goal is to make it to MOP next year through USAMO. It's gonna be a lot of work, but do you think that I should do MathWOOT 2 or OTIS? Personally, I felt that MathWOOT 1 taught me a lot but was more focused on computational - not sure how to split computation vs olympiad prep. So, for those who can address this question:

(1) How much compuational vs olympiad
(2) OTIS or MathWOOT 2 and why
6 replies
math_on_top
Sunday at 9:56 PM
MathCosine
11 minutes ago
Coordbashing = 0?
UberPiggy   11
N 12 minutes ago by UberPiggy
Hi,

I just received my USAJMO score distribution: 000 701 (very cursed I know)

The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
11 replies
UberPiggy
Apr 23, 2025
UberPiggy
12 minutes ago
OMMC TEAM
isache   14
N 34 minutes ago by isache
Hi everyone, im looking for an OMMC team. I have currently solved problems 1-16 with the exception of 13. Also, I would prefer if your team currently has 2 or 3 members. My stats:

133.5 on 10B this year
9 on aime this year, 8 the previous
24 on AMC 8
Orange County (CA) Mathcounts Champion in 8th and runner up in 7th
USCMC 4th place written 2nd place countdown (lost to tiger zhang)
UCSD HMM 5th place
SMT 15th place algebra round
nita main
3x AIME qual
3x AMC 10hr
14 replies
isache
Yesterday at 3:14 AM
isache
34 minutes ago
Random Math?
NASA1225   7
N 44 minutes ago by Ad_12
Does anybody here go to random math? If so, what was your experience like?
7 replies
NASA1225
Feb 6, 2022
Ad_12
44 minutes ago
Inspired by SXJX (12)2022 Q1167
sqing   1
N 2 hours ago by sqing
Source: Own
Let $ a,b,c>0 $. Prove that$$\frac{kabc-1} {abc(a+b+c+8(2k-1))}\leq \frac{1}{16 }$$Where $ k>\frac{1}{2}.$
1 reply
sqing
Yesterday at 4:01 AM
sqing
2 hours ago
Algebra manipulation excercise
Marinchoo   3
N 2 hours ago by compoly2010
Source: 2007 Bulgarian Autumn Math Competition, Problem 9.2
Let $a$, $b$, $c$ be real numbers, such that $a+b+c=0$ and $a^4+b^4+c^4=50$. Determine the value of $ab+bc+ca$.
3 replies
Marinchoo
Mar 17, 2022
compoly2010
2 hours ago
Numbers on a circle
navi_09220114   2
N 2 hours ago by ja.
Source: TASIMO 2025 Day 1 Problem 1
For a given positive integer $n$, determine the smallest integer $k$, such that it is possible to place numbers $1,2,3,\dots, 2n$ around a circle so that the sum of every $n$ consecutive numbers takes one of at most $k$ values.
2 replies
navi_09220114
Yesterday at 11:35 AM
ja.
2 hours ago
Inspired by 2007 Bulgarian
sqing   0
2 hours ago
Source: Own
Let $a$, $b$, $c$ be real numbers such that $a+b+c=0$ and $a^2+b^2+c^2+a^4+b^4+c^4=2$. Prove that $$ab+bc+ca=\frac{1-\sqrt 5}{2}$$Let $a$, $b$, $c$ be real numbers such that $a+b+c=0$ and $ab+bc+ca+a^2+b^2+c^2+a^4+b^4+c^4=2$. Prove that $$ab+bc+ca=\frac{1-\sqrt{17}}{4}$$
0 replies
1 viewing
sqing
2 hours ago
0 replies
Gives typical russian combinatorics vibes
Sadigly   4
N 4 hours ago by lbd4203
Source: Azerbaijan Senior MO 2025 P3
You are given a positive integer $n$. $n^2$ amount of people stand on coordinates $(x;y)$ where $x,y\in\{0;1;2;...;n-1\}$. Every person got a water cup and two people are considered to be neighbour if the distance between them is $1$. At the first minute, the person standing on coordinates $(0;0)$ got $1$ litres of water, and the other $n^2-1$ people's water cup is empty. Every minute, two neighbouring people are chosen that does not have the same amount of water in their water cups, and they equalize the amount of water in their water cups.

Prove that, no matter what, the person standing on the coordinates $(x;y)$ will not have more than $\frac1{x+y+1}$ litres of water.
4 replies
Sadigly
May 8, 2025
lbd4203
4 hours ago
Product of Sum
shobber   4
N 4 hours ago by alexanderchew
Source: CGMO 2006
Given that $x_{i}>0$, $i = 1, 2, \cdots, n$, $k \geq 1$. Show that: \[\sum_{i=1}^{n}\frac{1}{1+x_{i}}\cdot \sum_{i=1}^{n}x_{i}\leq \sum_{i=1}^{n}\frac{x_{i}^{k+1}}{1+x_{i}}\cdot \sum_{i=1}^{n}\frac{1}{x_{i}^{k}}\]
4 replies
shobber
Aug 9, 2006
alexanderchew
4 hours ago
Prove that two different boards can be obtained
hectorleo123   1
N 4 hours ago by Joalro178
Source: 2014 Peru Ibero TST P2
Let $n\ge 4$ be an integer. You have two $n\times n$ boards. Each board contains the numbers $1$ to $n^2$ inclusive, one number per square, arbitrarily arranged on each board. A move consists of exchanging two rows or two columns on the first board (no moves can be made on the second board). Show that it is possible to make a sequence of moves such that for all $1 \le i \le n$ and $1 \le j \le n$, the number that is in the $i-th$ row and $j-th$ column of the first board is different from the number that is in the $i-th$ row and $j-th$ column of the second board.
1 reply
hectorleo123
Sep 15, 2023
Joalro178
4 hours ago
Italian WinterCamps test07 Problem4
mattilgale   90
N 4 hours ago by mathwiz_1207
Source: ISL 2006, G3, VAIMO 2007/5
Let $ ABCDE$ be a convex pentagon such that
\[ \angle BAC = \angle CAD = \angle DAE\qquad \text{and}\qquad \angle ABC = \angle ACD = \angle ADE.
\]The diagonals $BD$ and $CE$ meet at $P$. Prove that the line $AP$ bisects the side $CD$.

Proposed by Zuming Feng, USA
90 replies
mattilgale
Jan 29, 2007
mathwiz_1207
4 hours ago
Iran TST P8
TheBarioBario   8
N 5 hours ago by Mysteriouxxx
Source: Iranian TST 2022 problem 8
In triangle $ABC$, with $AB<AC$, $I$ is the incenter, $E$ is the intersection of $A$-excircle and $BC$. Point $F$ lies on the external angle bisector of $BAC$ such that $E$ and $F$ lieas on the same side of the line $AI$ and $\angle AIF=\angle AEB$. Point $Q$ lies on $BC$ such that $\angle AIQ=90$. Circle $\omega_b$ is tangent to $FQ$ and $AB$ at $B$, circle $\omega_c$ is tangent to $FQ$ and $AC$ at $C$ and both circles pass through the inside of triangle $ABC$. if $M$ is the Midpoint od the arc $BC$, which does not contain $A$, prove that $M$ lies on the radical axis of $\omega_b$ and $\omega_c$.

Proposed by Amirmahdi Mohseni
8 replies
TheBarioBario
Apr 2, 2022
Mysteriouxxx
5 hours ago
IMO 2010 Problem 6
mavropnevma   42
N 5 hours ago by awesomeming327.
Let $a_1, a_2, a_3, \ldots$ be a sequence of positive real numbers, and $s$ be a positive integer, such that
\[a_n = \max \{ a_k + a_{n-k} \mid 1 \leq k \leq n-1 \} \ \textrm{ for all } \ n > s.\]
Prove there exist positive integers $\ell \leq s$ and $N$, such that
\[a_n = a_{\ell} + a_{n - \ell} \ \textrm{ for all } \ n \geq N.\]

Proposed by Morteza Saghafiyan, Iran
42 replies
mavropnevma
Jul 8, 2010
awesomeming327.
5 hours ago
k Sit Back and Enjoy the Problems
Binomial-theorem   230
N Jun 10, 2020 by Piano_Man123
Hi everyone! I was talking to djmathman earlier today, and we both noticed an increase in threads this contest season along the lines of “I suck at math because I didn’t do well on the AMC 10/12 test”. This unfortunate thought pattern seems to be growing a lot as people associate self-worth with contest math performance. However, while it’s true that people who often do great on math contests go on to do amazing things in mathematics, doing poorly on math contests does not make a person any less of a mathematician. Contest mathematics isn’t the “be all end all” of mathematics performance: it’s merely a gateway into getting people to think about more interesting problems.

One huge contributing factor to success in contest mathematics is having seen a lot of problems. Many contest math problems are very similar to problems on previous year’s contests, and therefore, understanding a lot of problem solving techniques is critical to success. (For instance, consider 2016 AMC 12A Problem #22 . Having seen 1987 AIME I Problem #7, a student could solve this problem almost immediately. On the other hand, a student who has never seen a problem like this before would be at a huge disadvantage, because, while they could come up with a solution on the fly, they don’t have a lot of time to do so.) Time pressure is a huge element of the AMC tests; these contests don’t always allow students to fully think about problems. When I do math problems, one of my favorite things to do is sit down with an idea and work with it for a while until I really fully grasp that concept, and the MAA does a fantastic job of starting conversations about tons of interesting things in mathematics. However, during the actual contest, competitors don’t have enough time to do so. If you can’t figure out how to solve a problem on the test, while it’s natural to feel bad initially (I’ve kicked myself many times over the “could’ve would’ve” problems), remember the main goal of doing mathematics: to understand and enjoy the problems. Read the different solutions on the forums, research a topic more which you may have been unfamiliar with, read a book. Then, next time around, not only will you nail the problem on the test, but you will also understand the underlying idea and intuition behind it.

I’m currently a senior in high school, and am almost officially finished with high school math competitions. I’ve participated in the AIME for the past 5 years along with MATHCOUNTS Nationals in 8th grade. I rarely share my scores with others on these tests for two reasons: (1) they’re usually below the first quartile of scores posted on AoPS and, most importantly, (2) I don’t compete in contest math for the sake of having a good score. I do it because I enjoy the problems, and the underlying mathematical ideas which accompany them. I’m an avid lover of Number Theory problems (shameless self promotion) and problems like 2016 AMC 12B Problem #22 excite me a lot, because this problem combined ideas about repeating decimals, order of a number, and divisibility. I didn’t solve this problem until after the test was over; however, when I did, I excitedly shared it with everyone in my school’s math club while teaching them some new things in number theory. Sharing this problem with my friends and teachers is the essence of the beauty of mathematics for me, because it lends itself well to collaboration in problem solving. When I find interesting problems like these, I often have them queued up to show to various people I encounter because I love inspiring others to have this level of inquisitiveness about a mathematical idea.

I’ve also been on the writing end of several math contests, including many Mock AMC exams on the AoPS forum, most notably the 2015 Mock AIME I. I also help write problems for the NIMO contest. My favorite thing about writing these problems is allowing competitors to think about mathematical concepts in new ways. For instance, this polynomial transformation problem taught a very important idea in algebra, which is building a polynomial out of the roots (an idea which was also featured in a similar USAMO problem before). Contributing to these discussions and having people solve my problems in many different ways is incredibly humbling for me, and is part of the beauty of contest mathematics. For more information on this, I highly recommend reading djmathman’s post here .

One of the great things about contest math is it starts these discussions. And, while tons of team contests like ARML and MATHCOUNTS try to inspire this level of collaboration and communication, it seems like it is often the missing link for many students who may be kicking themselves over a low score. Instead of thinking of a 96 on the AMC 10 as a complete failure and a wasted 2 years preparing for the exam, don’t let this score define you. Instead, learn new ideas from the problems and share them with those around you. Teaching may be a passion which is just mine, but I hope that you all can learn to truly enjoy the problems. Maybe you couldn’t solve 2016 AMC 12A Problem 23 . Read the solutions online, try to understand what’s going on in the 3d graph for this problem. Study equations like these more, and understand their graphs (this is especially important when discussing the space of matrices later down the road). If you want to go way above and beyond, maybe try to start understanding double integrals, as in va2010’s post in that thread. The main point is, this problem alone can generate tons of interesting discussions, and missing out on these are a shame. Getting a bad score isn’t a bad thing, but not learning from it surely is.

For another post in a similar vein, I highly recommend reading this post by hyperbolictangent. Although it approaches the manner from the perspective of students who are trying to prove themselves by commenting on how they underperformed on a contest, the ideas present in that post are incredibly relevant to this topic as well. (I highly recommend reading the whole thread too, as it has many different perspectives from many successful students).

Good luck on your future endeavors, and don’t forget to sit back and enjoy the problems!
230 replies
Binomial-theorem
Mar 13, 2016
Piano_Man123
Jun 10, 2020
Sit Back and Enjoy the Problems
G H J
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math129
700 posts
#428 • 2 Y
Y by Imayormaynotknowcalculus, samrocksnature
Imayormaynotknowcalculus wrote:

What I meant was $97\equiv 1\pmod{3}$.

LOL oops I got a 97.5 not 97
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zonee4
1258 posts
#429 • 1 Y
Y by samrocksnature
I got a wayyyyy worse score on the AMC 10
I got like a 66 or something
I'm bad at competition math but I do it just because I enjoy difficult things, always have. Its just a think about me. Probably started when I started playing suuuuuper hard video games. It feels almost euphoric. I go into the "zone" and it always feels great!
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superagh
1865 posts
#430 • 2 Y
Y by Imayormaynotknowcalculus, samrocksnature
Way to not give up!
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newphysicist101
206 posts
#431 • 2 Y
Y by OlympusHero, samrocksnature
Can the mods please lock this thread? I don't think it's going anywhere useful.
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hliu1
939 posts
#432 • 1 Y
Y by samrocksnature
I think it's going somewhere useful, particularly as a means of encouraging each other.
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zonee4
1258 posts
#433 • 2 Y
Y by samrocksnature, Mango247
hliu1 wrote:
I think it's going somewhere useful, particularly as a means of encouraging each other.

Same. That's pretty much the sole reason why I come here
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middletonkids
2460 posts
#434 • 1 Y
Y by samrocksnature
Just a question, but what is SSI?
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franzliszt
23531 posts
#435 • 2 Y
Y by Imayormaynotknowcalculus, samrocksnature
middletonkids wrote:
Just a question, but what is SSI?

I would avoid starting a discussion about that thank
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middletonkids
2460 posts
#436 • 1 Y
Y by samrocksnature
franzliszt wrote:
middletonkids wrote:
Just a question, but what is SSI?

I would avoid starting a discussion about that thank

But if I don't know what it is, I might start it on accident
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un57gcder1
312 posts
#437 • 1 Y
Y by samrocksnature
middletonkids wrote:
Just a question, but what is SSI?

Please read the announcement about SSI. Thanks!
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middletonkids
2460 posts
#438 • 1 Y
Y by samrocksnature
un57gcder1 wrote:
middletonkids wrote:
Just a question, but what is SSI?

Please read the announcement about SSI. Thanks!

I read it, but what does it stand for?
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aop2014
2416 posts
#439 • 1 Y
Y by samrocksnature
Just search SSI in the search function, now can we stop to avoid locking this
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OliverA
2588 posts
#440 • 1 Y
Y by samrocksnature
Please ask questions in a related thread. However, given that you already asked here: SSI stands from Summer STEM Institute
This post has been edited 2 times. Last edited by OliverA, Jun 10, 2020, 6:32 PM
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un57gcder1
312 posts
#441 • 1 Y
Y by samrocksnature
aop2014 wrote:
Just search SSI in the search function, now can we stop to avoid locking this
OliverA wrote:
Please ask that in a better suited thread. However, given that you already asked here: SSI stands from Summer STEM Institue

I already PMed him/her.

To get this back on topic:

This is kind of related. It actually helps you remember the similar problems from each contest that you saw.
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Piano_Man123
1774 posts
#442 • 2 Y
Y by samrocksnature, Mango247
The key is to not focus on the score, just focus on how well you enjoy the excellent problems!
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