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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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
Apr 2, 2025
0 replies
k i Peer-to-Peer Programs Forum
jwelsh   157
N Dec 11, 2023 by cw357
Many of our AoPS Community members share their knowledge with their peers in a variety of ways, ranging from creating mock contests to creating real contests to writing handouts to hosting sessions as part of our partnership with schoolhouse.world.

To facilitate students in these efforts, we have created a new Peer-to-Peer Programs forum. With the creation of this forum, we are starting a new process for those of you who want to advertise your efforts. These advertisements and ensuing discussions have been cluttering up some of the forums that were meant for other purposes, so we’re gathering these topics in one place. This also allows students to find new peer-to-peer learning opportunities without having to poke around all the other forums.

To announce your program, or to invite others to work with you on it, here’s what to do:

1) Post a new topic in the Peer-to-Peer Programs forum. This will be the discussion thread for your program.

2) Post a single brief post in this thread that links the discussion thread of your program in the Peer-to-Peer Programs forum.

Please note that we’ll move or delete any future advertisement posts that are outside the Peer-to-Peer Programs forum, as well as any posts in this topic that are not brief announcements of new opportunities. In particular, this topic should not be used to discuss specific programs; those discussions should occur in topics in the Peer-to-Peer Programs forum.

Your post in this thread should have what you're sharing (class, session, tutoring, handout, math or coding game/other program) and a link to the thread in the Peer-to-Peer Programs forum, which should have more information (like where to find what you're sharing).
157 replies
jwelsh
Mar 15, 2021
cw357
Dec 11, 2023
k i C&P posting recs by mods
v_Enhance   0
Jun 12, 2020
The purpose of this post is to lay out a few suggestions about what kind of posts work well for the C&P forum. Except in a few cases these are mostly meant to be "suggestions based on historical trends" rather than firm hard rules; we may eventually replace this with an actual list of firm rules but that requires admin approval :) That said, if you post something in the "discouraged" category, you should not be totally surprised if it gets locked; they are discouraged exactly because past experience shows they tend to go badly.
-----------------------------
1. Program discussion: Allowed
If you have questions about specific camps or programs (e.g. which classes are good at X camp?), these questions fit well here. Many camps/programs have specific sub-forums too but we understand a lot of them are not active.
-----------------------------
2. Results discussion: Allowed
You can make threads about e.g. how you did on contests (including AMC), though on AMC day when there is a lot of discussion. Moderators and administrators may do a lot of thread-merging / forum-wrangling to keep things in one place.
-----------------------------
3. Reposting solutions or questions to past AMC/AIME/USAMO problems: Allowed
This forum contains a post for nearly every problem from AMC8, AMC10, AMC12, AIME, USAJMO, USAMO (and these links give you an index of all these posts). It is always permitted to post a full solution to any problem in its own thread (linked above), regardless of how old the problem is, and even if this solution is similar to one that has already been posted. We encourage this type of posting because it is helpful for the user to explain their solution in full to an audience, and for future users who want to see multiple approaches to a problem or even just the frequency distribution of common approaches. We do ask for some explanation; if you just post "the answer is (B); ez" then you are not adding anything useful.

You are also encouraged to post questions about a specific problem in the specific thread for that problem, or about previous user's solutions. It's almost always better to use the existing thread than to start a new one, to keep all the discussion in one place easily searchable for future visitors.
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4. Advice posts: Allowed, but read below first
You can use this forum to ask for advice about how to prepare for math competitions in general. But you should be aware that this question has been asked many many times. Before making a post, you are encouraged to look at the following:
[list]
[*] Stop looking for the right training: A generic post about advice that keeps getting stickied :)
[*] There is an enormous list of links on the Wiki of books / problems / etc for all levels.
[/list]
When you do post, we really encourage you to be as specific as possible in your question. Tell us about your background, what you've tried already, etc.

Actually, the absolute best way to get a helpful response is to take a few examples of problems that you tried to solve but couldn't, and explain what you tried on them / why you couldn't solve them. Here is a great example of a specific question.
-----------------------------
5. Publicity: use P2P forum instead
See https://artofproblemsolving.com/community/c5h2489297_peertopeer_programs_forum.
Some exceptions have been allowed in the past, but these require approval from administrators. (I am not totally sure what the criteria is. I am not an administrator.)
-----------------------------
6. Mock contests: use Mock Contests forum instead
Mock contests should be posted in the dedicated forum instead:
https://artofproblemsolving.com/community/c594864_aops_mock_contests
-----------------------------
7. AMC procedural questions: suggest to contact the AMC HQ instead
If you have a question like "how do I submit a change of venue form for the AIME" or "why is my name not on the qualifiers list even though I have a 300 index", you would be better off calling or emailing the AMC program to ask, they are the ones who can help you :)
-----------------------------
8. Discussion of random math problems: suggest to use MSM/HSM/HSO instead
If you are discussing a specific math problem that isn't from the AMC/AIME/USAMO, it's better to post these in Middle School Math, High School Math, High School Olympiads instead.
-----------------------------
9. Politics: suggest to use Round Table instead
There are important conversations to be had about things like gender diversity in math contests, etc., for sure. However, from experience we think that C&P is historically not a good place to have these conversations, as they go off the rails very quickly. We encourage you to use the Round Table instead, where it is much more clear that all posts need to be serious.
-----------------------------
10. MAA complaints: discouraged
We don't want to pretend that the MAA is perfect or that we agree with everything they do. However, we chose to discourage this sort of behavior because in practice most of the comments we see are not useful and some are frankly offensive.
[list] [*] If you just want to blow off steam, do it on your blog instead.
[*] When you have criticism, it should be reasoned, well-thought and constructive. What we mean by this is, for example, when the AOIME was announced, there was great outrage about potential cheating. Well, do you really think that this is something the organizers didn't think about too? Simply posting that "people will cheat and steal my USAMOO qualification, the MAA are idiots!" is not helpful as it is not bringing any new information to the table.
[*] Even if you do have reasoned, well-thought, constructive criticism, we think it is actually better to email it the MAA instead, rather than post it here. Experience shows that even polite, well-meaning suggestions posted in C&P are often derailed by less mature users who insist on complaining about everything.
[/list]
-----------------------------
11. Memes and joke posts: discouraged
It's fine to make jokes or lighthearted posts every so often. But it should be done with discretion. Ideally, jokes should be done within a longer post that has other content. For example, in my response to one user's question about olympiad combinatorics, I used a silly picture of Sogiita Gunha, but it was done within a context of a much longer post where it was meant to actually make a point.

On the other hand, there are many threads which consist largely of posts whose only content is an attached meme with the word "MAA" in it. When done in excess like this, the jokes reflect poorly on the community, so we explicitly discourage them.
-----------------------------
12. Questions that no one can answer: discouraged
Examples of this: "will MIT ask for AOIME scores?", "what will the AIME 2021 cutoffs be (asked in 2020)", etc. Basically, if you ask a question on this forum, it's better if the question is something that a user can plausibly answer :)
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13. Blind speculation: discouraged
Along these lines, if you do see a question that you don't have an answer to, we discourage "blindly guessing" as it leads to spreading of baseless rumors. For example, if you see some user posting "why are there fewer qualifiers than usual this year?", you should not reply "the MAA must have been worried about online cheating so they took fewer people!!". Was sich überhaupt sagen lässt, lässt sich klar sagen; und wovon man nicht reden kann, darüber muss man schweigen.
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14. Discussion of cheating: strongly discouraged
If you have evidence or reasonable suspicion of cheating, please report this to your Competition Manager or to the AMC HQ; these forums cannot help you.
Otherwise, please avoid public discussion of cheating. That is: no discussion of methods of cheating, no speculation about how cheating affects cutoffs, and so on --- it is not helpful to anyone, and it creates a sour atmosphere. A longer explanation is given in Seriously, please stop discussing how to cheat.
-----------------------------
15. Cutoff jokes: never allowed
Whenever the cutoffs for any major contest are released, it is very obvious when they are official. In the past, this has been achieved by the numbers being posted on the official AMC website (here) or through a post from the AMCDirector account.

You must never post fake cutoffs, even as a joke. You should also refrain from posting cutoffs that you've heard of via email, etc., because it is better to wait for the obvious official announcement. A longer explanation is given in A Treatise on Cutoff Trolling.
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16. Meanness: never allowed
Being mean is worse than being immature and unproductive. If another user does something which you think is inappropriate, use the Report button to bring the post to moderator attention, or if you really must reply, do so in a way that is tactful and constructive rather than inflammatory.
-----------------------------

Finally, we remind you all to sit back and enjoy the problems. :D

-----------------------------
(EDIT 2024-09-13: AoPS has asked to me to add the following item.)

Advertising paid program or service: never allowed

Per the AoPS Terms of Service (rule 5h), general advertisements are not allowed.

While we do allow advertisements of official contests (at the MAA and MATHCOUNTS level) and those run by college students with at least one successful year, any and all advertisements of a paid service or program is not allowed and will be deleted.
0 replies
v_Enhance
Jun 12, 2020
0 replies
k i Stop looking for the "right" training
v_Enhance   50
N Oct 16, 2017 by blawho12
Source: Contest advice
EDIT 2019-02-01: https://blog.evanchen.cc/2019/01/31/math-contest-platitudes-v3/ is the updated version of this.

EDIT 2021-06-09: see also https://web.evanchen.cc/faq-contest.html.

Original 2013 post
50 replies
v_Enhance
Feb 15, 2013
blawho12
Oct 16, 2017
Some nice summations
amitwa.exe   30
N 7 minutes ago by P162008
Problem 1: $\Omega=\left(\sum_{0\le i\le j\le k}^{\infty} \frac{1}{3^i\cdot4^j\cdot5^k}\right)\left(\mathop{{\sum_{i=0}^{\infty}\sum_{j=0}^{\infty}\sum_{k=0}^{\infty}}}_{i\neq j\neq k}\frac{1}{3^i\cdot3^j\cdot3^k}\right)=?$
30 replies
+1 w
amitwa.exe
May 24, 2024
P162008
7 minutes ago
Prove a polynomial has a nonreal root
KevinYang2.71   46
N 43 minutes ago by megarnie
Source: USAMO 2025/2
Let $n$ and $k$ be positive integers with $k<n$. Let $P(x)$ be a polynomial of degree $n$ with real coefficients, nonzero constant term, and no repeated roots. Suppose that for any real numbers $a_0,\,a_1,\,\ldots,\,a_k$ such that the polynomial $a_kx^k+\cdots+a_1x+a_0$ divides $P(x)$, the product $a_0a_1\cdots a_k$ is zero. Prove that $P(x)$ has a nonreal root.
46 replies
1 viewing
KevinYang2.71
Mar 20, 2025
megarnie
43 minutes ago
9 USA(J)MO Grading Poll
elasticwealth   2
N an hour ago by MrMustache
Please vote honestly. If you did not compete in the USA(J)MO, please do not vote.
2 replies
elasticwealth
an hour ago
MrMustache
an hour ago
Combo problem
soryn   3
N an hour ago by soryn
The school A has m1 boys and m2 girls, and ,the school B has n1 boys and n2 girls. Each school is represented by one team formed by p students,boys and girls. If f(k) is the number of cases for which,the twice schools has,togheter k girls, fund f(k) and the valute of k, for which f(k) is maximum.
3 replies
soryn
Yesterday at 6:33 AM
soryn
an hour ago
Looking for the smallest ghost
Justpassingby   5
N an hour ago by venhancefan777
Source: 2021 Mexico Center Zone Regional Olympiad, problem 1
Let $p$ be an odd prime number. Let $S=a_1,a_2,\dots$ be the sequence defined as follows: $a_1=1,a_2=2,\dots,a_{p-1}=p-1$, and for $n\ge p$, $a_n$ is the smallest integer greater than $a_{n-1}$ such that in $a_1,a_2,\dots,a_n$ there are no arithmetic progressions of length $p$. We say that a positive integer is a ghost if it doesn’t appear in $S$.
What is the smallest ghost that is not a multiple of $p$?

Proposed by Guerrero
5 replies
Justpassingby
Jan 17, 2022
venhancefan777
an hour ago
non-symmetric ineq (for girls)
easternlatincup   36
N an hour ago by Tony_stark0094
Source: Chinese Girl's MO 2007
For $ a,b,c\geq 0$ with $ a+b+c=1$, prove that

$ \sqrt{a+\frac{(b-c)^2}{4}}+\sqrt{b}+\sqrt{c}\leq \sqrt{3}$
36 replies
easternlatincup
Dec 30, 2007
Tony_stark0094
an hour ago
SL Difficulty Level
MajesticCheese   5
N 2 hours ago by llddmmtt1
Is there a rough difficulty comparison between IMO shortlist questions and USAMO questions? For example,

SL 1, 2, 3 -> USAMO P1
SL 4, 5, 6 -> USAMO P2
SL 7, 8, 9 -> USAMO P3

(This is just my guess; probably not correct)

Also feel free to compare it with other competitions(like the jmo) as well! :-D
5 replies
MajesticCheese
Apr 20, 2025
llddmmtt1
2 hours ago
Metals cutoff prediction; mop colors prediction
mulberrykid   12
N 3 hours ago by ihatemath123
For USAMO and JMO,

what will the cutoff for different metals:

1. Gold: ?
2. Silver:?
3. Bronze:?


JMO:
Honors: ?
High Honors:?

MOP colors:
Black:?
Blue:?
Green:?
Orange:?
Red: ?




12 replies
mulberrykid
Yesterday at 8:23 PM
ihatemath123
3 hours ago
0 on JMO P2
dogeA   25
N 5 hours ago by wsgcuhladoo
Source: USAJMO 2025 Problem 2
I got a 0 on this problem but I'm not really sure why, as I should be at least on the right track? Can someone tell me why I got a 0?
25 replies
1 viewing
dogeA
Yesterday at 8:53 PM
wsgcuhladoo
5 hours ago
usamOOK geometry
KevinYang2.71   98
N 5 hours ago by elasticwealth
Source: USAMO 2025/4, USAJMO 2025/5
Let $H$ be the orthocenter of acute triangle $ABC$, let $F$ be the foot of the altitude from $C$ to $AB$, and let $P$ be the reflection of $H$ across $BC$. Suppose that the circumcircle of triangle $AFP$ intersects line $BC$ at two distinct points $X$ and $Y$. Prove that $C$ is the midpoint of $XY$.
98 replies
KevinYang2.71
Mar 21, 2025
elasticwealth
5 hours ago
USA(J)MO scores will be released today
profhong   29
N 6 hours ago by LearnMath_105
The awards will be out next week.
Best luck!
29 replies
profhong
Yesterday at 5:21 PM
LearnMath_105
6 hours ago
Subset coloring
v_Enhance   73
N Yesterday at 6:52 PM by Maximilian113
Source: USAMO 2015 Problem 3
Let $S = \left\{ 1,2,\dots,n \right\}$, where $n \ge 1$. Each of the $2^n$ subsets of $S$ is to be colored red or blue. (The subset itself is assigned a color and not its individual elements.) For any set $T \subseteq S$, we then write $f(T)$ for the number of subsets of $T$ that are blue.

Determine the number of colorings that satisfy the following condition: for any subsets $T_1$ and $T_2$ of $S$, \[ f(T_1)f(T_2) = f(T_1 \cup T_2)f(T_1 \cap T_2). \]
73 replies
v_Enhance
Apr 28, 2015
Maximilian113
Yesterday at 6:52 PM
p^k divides term of sequence
KevinYang2.71   34
N Yesterday at 4:35 PM by cursed_tangent1434
Source: USAJMO 2024/3
Let $a(n)$ be the sequence defined by $a(1)=2$ and $a(n+1)=(a(n))^{n+1}-1$ for each integer $n\geq 1$. Suppose that $p>2$ is a prime and $k$ is a positive integer. Prove that some term of the sequence $a(n)$ is divisible by $p^k$.

Proposed by John Berman
34 replies
KevinYang2.71
Mar 20, 2024
cursed_tangent1434
Yesterday at 4:35 PM
AMC and JMO qual question
HungryCalculator   4
N Yesterday at 12:04 PM by eyzMath
Say that on the AMC 10, you do better on the A than the B, but you still qualify for AIME thru both. Then after your AIME, it turns out that you didn’t make JMO through the A+AIME index but you did pass the threshold for the B+AIME index.

does MAA consider your B+AIME index over the A+AIME index and consider you a JMO qualifier even tho Your A test score was higher?

4 replies
HungryCalculator
Apr 17, 2025
eyzMath
Yesterday at 12:04 PM
Find the circumradius of some triangle.
mathmanman   3
N Oct 3, 2020 by snakeaid
Source: Tuymaada 2004, day 1, problem 3. - Authors : F. Bakharev, F. Petrov.
An acute triangle $ABC$ is inscribed in a circle of radius 1 with centre $O;$ all the angles of $ABC$ are greater than $45^\circ.$
$B_{1}$ is the foot of perpendicular from $B$ to $CO,$ $B_{2}$ is the foot of perpendicular from $B_{1}$ to $AC.$
Similarly, $C_{1}$ is the foot of perpendicular from $C$ to $BO,$ $C_{2}$ is the foot of perpendicular from $C_{1}$ to $AB.$
The lines $B_{1}B_{2}$ and $C_{1}C_{2}$ intersect at $A_{3}.$ The points $B_{3}$ and $C_{3}$ are defined in the same way.
Find the circumradius of triangle $A_{3}B_{3}C_{3}.$

Proposed by F.Bakharev, F.Petrov
3 replies
mathmanman
May 25, 2007
snakeaid
Oct 3, 2020
Find the circumradius of some triangle.
G H J
Source: Tuymaada 2004, day 1, problem 3. - Authors : F. Bakharev, F. Petrov.
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mathmanman
1444 posts
#1 • 1 Y
Y by Adventure10
An acute triangle $ABC$ is inscribed in a circle of radius 1 with centre $O;$ all the angles of $ABC$ are greater than $45^\circ.$
$B_{1}$ is the foot of perpendicular from $B$ to $CO,$ $B_{2}$ is the foot of perpendicular from $B_{1}$ to $AC.$
Similarly, $C_{1}$ is the foot of perpendicular from $C$ to $BO,$ $C_{2}$ is the foot of perpendicular from $C_{1}$ to $AB.$
The lines $B_{1}B_{2}$ and $C_{1}C_{2}$ intersect at $A_{3}.$ The points $B_{3}$ and $C_{3}$ are defined in the same way.
Find the circumradius of triangle $A_{3}B_{3}C_{3}.$

Proposed by F.Bakharev, F.Petrov
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Erken
1363 posts
#2 • 1 Y
Y by Adventure10
Let $ C_1C_2$ intersect AC at point B' and $ B_1B_2$ intersect AB at point C'. It is easy to prove that BB' is perpendicular to AC:
Let $ \measuredangle C_1BC=a$ then $ \measuredangle A=90^{\circ}-a$ and $ \measuredangle C_1B^{\prime}C=a$, so that $ BB^{\prime}C_1C$ is an inscribed quadriterial and $ \measuredangle BB^{\prime}C=90^{\circ}$.
So $ A_3$ is the orthocenter of triangle $ AC^{\prime}B^{\prime}$. The same way $ B_3$ and $ C_3$ are orthocentres of triangles $ BC^{\prime}A^{\prime}$ and $ CA^{\prime}B^{\prime}$ respectively.
It is easy to prove that $ A_3B_3C_3$ and $ A^{\prime}B^{\prime}C^{\prime}$ are congruent triangles ($ A^{\prime}B^{\prime}A_3B_3$ is parallelogram) but the circumradius of A'B'C' is $ \frac12$.
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Erken
1363 posts
#3 • 2 Y
Y by Adventure10, Mango247
Just want to post a picture to this great problem:
Image not found
P.S.This problem is great,as all geometry problems from Tuymaada. :wink:.
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snakeaid
125 posts
#4
Y by
Complex numbers
This post has been edited 1 time. Last edited by snakeaid, Oct 3, 2020, 12:30 PM
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