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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 March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/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
Mar 2, 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
Diophantine equation with large moduli
Assassino9931   2
N 30 minutes ago by Assassino9931
Source: Bulgaria, Concours Generale Minko Balkanski 2024
Solve in positive integers $2^x - 23^y = 9$.
2 replies
Assassino9931
4 hours ago
Assassino9931
30 minutes ago
Problem 4
blug   0
31 minutes ago
Source: Polish Junior Math Olympiad Finals 2025
In a rhombus $ABCD$, angle $\angle ABC=100^{\circ}$. Point $P$ lies on $CD$ such that $\angle PBC=20^{\circ}$. Line parallel to $AD$ passing trough $P$ intersects $AC$ at $Q$. Prove that $BP=AQ$.
0 replies
blug
31 minutes ago
0 replies
Problem 3
blug   0
33 minutes ago
Source: Polish Junior Math Olympiad Finals 2025
Find all primes $(p, q, r)$ such that
$$pq+4=r^4.$$
0 replies
blug
33 minutes ago
0 replies
Problem 1
blug   0
35 minutes ago
Source: Polish Junior Math Olympiad Finals 2025
Do there exists a tetrahedron, in which the lenghts of the edges are six different integers such that their sum is 25?
0 replies
blug
35 minutes ago
0 replies
A two-variable & non-homogenous inequality that seems hard to me
MyLifeMyChoice   3
N 44 minutes ago by Radin_
Source: Developing from a larger, three-variable one
For $a,b>0$, prove/disprove the following claim: :maybe:

$a^3b^3+\frac{1}{a^3}+\frac{1}{b^3}+3\stackrel{?}{\ge}a^2b+b^2a+\frac{1}{a^2b}+\frac{1}{b^2a}+\frac{a}{b}+\frac{b}{a}$
3 replies
MyLifeMyChoice
Mar 13, 2025
Radin_
44 minutes ago
exponential diophantine with factorials
skellyrah   4
N an hour ago by InftyByond
find all non negative integers (x,y) such that $$ x! + y! = 2025^x + xy$$
4 replies
skellyrah
Feb 24, 2025
InftyByond
an hour ago
Point satisfies triple property
62861   35
N an hour ago by Sanjana42
Source: USA Winter Team Selection Test #2 for IMO 2018, Problem 2
Let $ABCD$ be a convex cyclic quadrilateral which is not a kite, but whose diagonals are perpendicular and meet at $H$. Denote by $M$ and $N$ the midpoints of $\overline{BC}$ and $\overline{CD}$. Rays $MH$ and $NH$ meet $\overline{AD}$ and $\overline{AB}$ at $S$ and $T$, respectively. Prove that there exists a point $E$, lying outside quadrilateral $ABCD$, such that
[list]
[*] ray $EH$ bisects both angles $\angle BES$, $\angle TED$, and
[*] $\angle BEN = \angle MED$.
[/list]

Proposed by Evan Chen
35 replies
62861
Jan 22, 2018
Sanjana42
an hour ago
Prove concyclic and tangency
syk0526   40
N an hour ago by Ilikeminecraft
Source: Japan Olympiad Finals 2014, #4
Let $ \Gamma $ be the circumcircle of triangle $ABC$, and let $l$ be the tangent line of $\Gamma $ passing $A$. Let $ D, E $ be the points each on side $AB, AC$ such that $ BD : DA= AE : EC $. Line $ DE $ meets $\Gamma $ at points $ F, G $. The line parallel to $AC$ passing $ D $ meets $l$ at $H$, the line parallel to $AB$ passing $E$ meets $l$ at $I$. Prove that there exists a circle passing four points $ F, G, H, I $ and tangent to line $ BC$.
40 replies
syk0526
May 17, 2014
Ilikeminecraft
an hour ago
p^2+3*p*q+q^2
mathbetter   0
2 hours ago
\[
\text{Find all prime numbers } (p, q) \text{ such that } p^2 + 3pq + q^2 \text{ is a fifth power of an integer.}
\]
0 replies
mathbetter
2 hours ago
0 replies
two sequences of positive integers and inequalities
rmtf1111   49
N 2 hours ago by dolphinday
Source: EGMO 2019 P5
Let $n\ge 2$ be an integer, and let $a_1, a_2, \cdots , a_n$ be positive integers. Show that there exist positive integers $b_1, b_2, \cdots, b_n$ satisfying the following three conditions:

$\text{(A)} \ a_i\le b_i$ for $i=1, 2, \cdots , n;$

$\text{(B)} \ $ the remainders of $b_1, b_2, \cdots, b_n$ on division by $n$ are pairwise different; and

$\text{(C)} \ $ $b_1+b_2+\cdots b_n \le n\left(\frac{n-1}{2}+\left\lfloor \frac{a_1+a_2+\cdots a_n}{n}\right \rfloor \right)$

(Here, $\lfloor x \rfloor$ denotes the integer part of real number $x$, that is, the largest integer that does not exceed $x$.)
49 replies
rmtf1111
Apr 10, 2019
dolphinday
2 hours ago
AIME score for college apps
Happyllamaalways   56
N 4 hours ago by Countmath1
What good colleges do I have a chance of getting into with an 11 on AIME? (Any chances for Princeton)

Also idk if this has weight but I had the highest AIME score in my school.
56 replies
Happyllamaalways
Mar 13, 2025
Countmath1
4 hours ago
MIT Beaverworks Summer Institute
PowerOfPi_09   0
4 hours ago
Hi! I was wondering if anyone here has completed this program, and if so, which track did you choose? Do rising juniors have a chance, or is it mainly rising seniors that they accept? Also, how long did it take you to complete the prerequisites?
Thanks!
0 replies
PowerOfPi_09
4 hours ago
0 replies
Convolution of order f(n)
trumpeter   70
N 4 hours ago by HamstPan38825
Source: 2019 USAMO Problem 1
Let $\mathbb{N}$ be the set of positive integers. A function $f:\mathbb{N}\to\mathbb{N}$ satisfies the equation \[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]for all positive integers $n$. Given this information, determine all possible values of $f(1000)$.

Proposed by Evan Chen
70 replies
1 viewing
trumpeter
Apr 17, 2019
HamstPan38825
4 hours ago
k HOT TAKE: MIT SHOULD NOT RELEASE THEIR DECISIONS ON PI DAY
alcumusftwgrind   8
N Today at 10:13 AM by maxamc
rant lol

Imagine a poor senior waiting for their MIT decisions just to have their hopes CRUSHED on 3/14 and they can't even celebrate pi day...

and even worse, this year's pi day is special because this year is a very special number...

8 replies
alcumusftwgrind
Today at 2:11 AM
maxamc
Today at 10:13 AM
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
G H BBookmark kLocked kLocked NReply
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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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