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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Jul 1, 2025
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
and train with the best! Please note that early bird pricing ends August 19th!
Are you tired of the heat and thinking about Fall? You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US.

Our full course list for upcoming classes is below:
All classes start 7:30pm ET/4:30pm PT unless otherwise noted.

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0 replies
jwelsh
Jul 1, 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.
-----------------------------
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 :)
-----------------------------
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.
-----------------------------
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.
-----------------------------
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
Concurrency property in an earlier configuration
RANDOM__USER   0
4 minutes ago
Source: Own
Let \(D\) be an arbitrary point on the side \(BC\) in a triangle \(\triangle{ABC}\). Let \(E\) and \(F\) be the intersection of the lines parallel to \(AC\) and \(AB\) through \(D\) with \(AB\) and \(AC\). Let \(G\) be the intersection of \((AFE)\) with \((ABC)\). Let \(M\) be the midpoint of \(BC\) and \(X\) the intersection of \(AM\) with \((ABC)\). Let \(J\) be the intersection of \((XFG)\) with \(AC\). Prove that \(XB\), \(AD\) and \(JM\) are concurrent at \(P\).

IMAGE

Note: This is another property of a configuration I posted before where one needed to prove that \(X, D\) and \(G\) are collinear. There are surprisingly many properties in the configuration posted earlier :P
0 replies
RANDOM__USER
4 minutes ago
0 replies
Sum of GCD
Timta27   0
5 minutes ago
Source: own
Prove that there are infinitely many pairs of integers $(n,k),$ where $3 \leq k+2 \leq n$, such that it is possible to find three natural numbers $a,b,c$ ($k \leq a \leq b \leq c <n $) such that $GCD(a,b)+GCD(a,c)+GCD(b,c) = n$.
0 replies
Timta27
5 minutes ago
0 replies
BK.CJ=BJ.CH
truongphatt2668   2
N 11 minutes ago by aqwxderf
Let triangle $ABC$ has $D$ on $A$-angle bisector such that $\widehat{BDC} = 90^o$. A line passes $A$ perpendicular to $AD$ cuts $BD,CD$ at $E,F$, respectively. $I$ is the intersection of $AB$ and $(ADF)$. $J$ is defined similarly. $IC$ and $JB$ cuts $(ADF), (ADE)$ at $H,K$, respectively. Prove that: $BK.CJ = BJ.CH$.
2 replies
truongphatt2668
Today at 9:33 AM
aqwxderf
11 minutes ago
International competition SRMC 2004 P-2
Ovchinnikov Denis   3
N 33 minutes ago by mahyar_ais
find all primes $p$, for which exist natural numbers, such that $p=m^2+n^2$ and $p|(m^3+n^3-4)$.
3 replies
+1 w
Ovchinnikov Denis
Sep 7, 2010
mahyar_ais
33 minutes ago
how long to study for AMC
AdrienMarieLegendre   10
N 3 hours ago by Bread10
This might not be the right question to ask, but I want to know for reference. I will be taking the AMC 10 in november, and my current score on practice tests is 50. Around how long do you think I should study per day, and how much time did you put into studying daily to make AIME?
10 replies
1 viewing
AdrienMarieLegendre
Yesterday at 11:27 PM
Bread10
3 hours ago
Subsets with Consecutive Numbers
worthawholebean   19
N Today at 1:09 PM by SomeonecoolLovesMaths
Source: AIME 2009II Problem 6
Let $ m$ be the number of five-element subsets that can be chosen from the set of the first $ 14$ natural numbers so that at least two of the five numbers are consecutive. Find the remainder when $ m$ is divided by $ 1000$.
19 replies
worthawholebean
Apr 2, 2009
SomeonecoolLovesMaths
Today at 1:09 PM
Green and red marbles [2011.II.7]
#H34N1   11
N Today at 1:01 PM by SomeonecoolLovesMaths
Ed has five identical green marbles and a large supply of identical red marbles. He arranges the green marbles and some of the red marbles in a row and finds that the number of marbles whose right hand neighbor is the same color as themselves equals the number of marbles whose right hand neighbor is the other color. An example of such an arrangement is GGRRRGGRG. Let $m$ be the maximum number of red marbles for which Ed can make such an arrangement, and let $N$ be the number of ways in which Ed can arrange the $m+5$ marbles to satisfy the requirement. Find the remainder when $N$ is divided by 1000.
11 replies
#H34N1
Mar 31, 2011
SomeonecoolLovesMaths
Today at 1:01 PM
Summer Mission Math Tournament (SMMT)
cowstalker   0
Today at 6:35 AM
Source: Mission San Jose Math Club
Hey everyone, MSJ Math Club is excited to announce the 5th annual Summer Mission Math Tournament (SMMT) on Sunday, August 3rd! Like previous years, we will have both individual and team rounds:


The Individual Round will be a competitive math-style round, with 2 divisions. The Warrior division will be similar in difficulty to the AMC 10, and the Champion division will be similar in difficulty to the AIME.

In the Team Rounds, you'll be able to work in a team of up to 4 people. There will be a Guts Round, in which your team will work on 27 competitive-math style problems divided into 9 sets of 3, one set at a time. There will also be an Estimathon Round, which consists of 15 Fermi-style estimation questions. For example, you may be asked: “How many laps of a standard track is equivalent to the circumference of Jupiter?”


There will be prizes as always, and anyone who participates will receive a FREE Brilliant Premium Subscription!

If you’re interested, please register on the Sign Up Form and join the SMMT Discord Server . For more info about the contest, check out the SMMT 2025 Info Doc.

We look forward to seeing you (virtually) at SMMT 2025!

0 replies
cowstalker
Today at 6:35 AM
0 replies
Moving P(o)in(t)s
bobthegod78   74
N Today at 2:45 AM by mathprodigy2011
Source: USAJMO 2021/4
Carina has three pins, labeled $A, B$, and $C$, respectively, located at the origin of the coordinate plane. In a move, Carina may move a pin to an adjacent lattice point at distance $1$ away. What is the least number of moves that Carina can make in order for triangle $ABC$ to have area 2021?

(A lattice point is a point $(x, y)$ in the coordinate plane where $x$ and $y$ are both integers, not necessarily positive.)
74 replies
bobthegod78
Apr 15, 2021
mathprodigy2011
Today at 2:45 AM
Getting accepted to PROMYS
AdrienMarieLegendre   5
N Today at 1:32 AM by Narwhal234
what are your tips for getting accepted into promys?? how can I prepare for the application, and what should I do to develop 'mathematical creativity' so I could tackle the problems easier and come up with interesting solutions?
5 replies
AdrienMarieLegendre
Yesterday at 5:48 PM
Narwhal234
Today at 1:32 AM
Short and fun.
solafidefarms   14
N Yesterday at 11:36 PM by EVS383
Source: 2006 AIME II 14
Let $S_n$ be the sum of the reciprocals of the non-zero digits of the integers from 1 to $10^n$ inclusive. Find the smallest positive integer $n$ for which $S_n$ is an integer.
14 replies
solafidefarms
Mar 28, 2006
EVS383
Yesterday at 11:36 PM
force overlay inversion vibes
v4913   66
N Yesterday at 10:29 PM by vincentwant
Source: USAMO 2023/6
Let $ABC$ be a triangle with incenter $I$ and excenters $I_a$, $I_b$, and $I_c$ opposite $A$, $B$, and $C$, respectively. Let $D$ be an arbitrary point on the circumcircle of $\triangle{ABC}$ that does not lie on any of the lines $II_a$, $I_bI_c$, or $BC$. Suppose the circumcircles of $\triangle{DII_a}$ and $\triangle{DI_bI_c}$ intersect at two distinct points $D$ and $F$. If $E$ is the intersection of lines $DF$ and $BC$, prove that $\angle{BAD} = \angle{EAC}$.

Proposed by Zach Chroman
66 replies
1 viewing
v4913
Mar 23, 2023
vincentwant
Yesterday at 10:29 PM
Digit switching
Th3Numb3rThr33   101
N Yesterday at 7:38 PM by ray66
Source: 2018 USAJMO #1
For each positive integer $n$, find the number of $n$-digit positive integers that satisfy both of the following conditions:
[list]
[*] no two consecutive digits are equal, and
[*] the last digit is a prime.
[/list]
101 replies
Th3Numb3rThr33
Apr 18, 2018
ray66
Yesterday at 7:38 PM
USAMTS and AMC 10?
HungryCalculator   8
N Yesterday at 5:35 PM by HungryCalculator
Say you take the USAMTS and AMC10, and you qualify for AIME through both pathways.

Does your JMO qualification now depend on your AMC10 pathway (AMC + AIME), or just the 9+ on AIME required for JMO Qual through the USAMTS + AIME pathway?

Are you even allowed to take both USAMTS and AMC10 in the first place?
8 replies
HungryCalculator
Jul 9, 2025
HungryCalculator
Yesterday at 5:35 PM
A second final attempt to make a combinatorics problem
JARP091   2
N May 29, 2025 by JARP091
Source: At the time of writing this problem I do not know the source if any
Arthur Morgan is playing a game.

He has $n$ eggs, each with a hardness value $k_1, k_2, \dots, k_n$, where $\{k_1, k_2, \dots, k_n\}$ is a permutation of the set $\{1, 2, \dots, n\}$. He is throwing the eggs from an $m$-floor building.

When the $i$-th egg is dropped from the $j$-th floor, its new hardness becomes
\[
\left\lfloor \frac{k_i}{j+1} \right\rfloor.
\]If $\left\lfloor \frac{k_i}{j+1} \right\rfloor = 0$, then the egg breaks and cannot be used again.

Arthur can drop each egg from a particular floor at most once.
For which values of $n$ and $m$ can Arthur always determine the correct ordering of the eggs according to their initial hardness values?
Note: The problem might be wrong or too easy
2 replies
JARP091
May 25, 2025
JARP091
May 29, 2025
A second final attempt to make a combinatorics problem
G H J
Source: At the time of writing this problem I do not know the source if any
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
JARP091
124 posts
#1
Y by
Arthur Morgan is playing a game.

He has $n$ eggs, each with a hardness value $k_1, k_2, \dots, k_n$, where $\{k_1, k_2, \dots, k_n\}$ is a permutation of the set $\{1, 2, \dots, n\}$. He is throwing the eggs from an $m$-floor building.

When the $i$-th egg is dropped from the $j$-th floor, its new hardness becomes
\[
\left\lfloor \frac{k_i}{j+1} \right\rfloor.
\]If $\left\lfloor \frac{k_i}{j+1} \right\rfloor = 0$, then the egg breaks and cannot be used again.

Arthur can drop each egg from a particular floor at most once.
For which values of $n$ and $m$ can Arthur always determine the correct ordering of the eggs according to their initial hardness values?
Note: The problem might be wrong or too easy
This post has been edited 1 time. Last edited by JARP091, May 25, 2025, 2:46 PM
Reason: Wrongly LaTeXted
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Bump for this problem
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Drop something from 1, if it breaks then its 0

if it doesnt break, it is currently 1, we have one more one, and we have a number we are trying to find out

we cant drop the number we are interested in from floor 1, otherwise we lose information

hence drop another egg from floor 2, if it doesnt break, it was 3, we started with a 2, and ther last egg is 1, if it breaks, then we either dropped a 1, or we dropped a 2, and so the possible outputs are (1,0,2) (1,0,3) (1,0,1), now we cant figure out what state the last egg is in, so it is impossible.

For n $>$ 3, n = 3 is a subproblem that cannot be solved.

Hence only possible solutions are:

i) n = 1, m $\geq$ 1

ii) n = 2, m $\geq$ 2
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