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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jun 2, 2025
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this 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 a transformative 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][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/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
Jun 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.
-----------------------------
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
2017 preRMO p2, a\sqrt{a}+b\sqrt{b}=183, a\sqrt{b}+b\sqrt{a} = 182
parmenides51   9
N an hour ago by fathersayno
Suppose $a, b$ are positive real numbers such that $a\sqrt{a} + b\sqrt{b} = 183, a\sqrt{b} + b\sqrt{a} = 182$. Find $\frac95 (a + b)$.
9 replies
parmenides51
Aug 9, 2019
fathersayno
an hour ago
Increasing/decreasing intervals
Antony105   8
N 2 hours ago by HAL9000sk
On the graph of $f(x)$, are the intervals on which it is increasing/decreasing open or closed? For instance, for $f(x) = x^2$, is it increasing on $(0,\infty)$ or $[0,\infty)$?
8 replies
Antony105
Yesterday at 9:12 PM
HAL9000sk
2 hours ago
Inequalities
sqing   1
N 3 hours ago by pooh123
Let $ x,y \geq 0 ,  \frac{x}{x^2+y}+\frac{y}{x+y^2} \geq 2 .$ Prove that
$$ (x-\frac{1}{2})^2+(y+\frac{1}{2})^2 \leq \frac{5}{4} $$$$ (x-1)^2+(y+1)^2 \leq  \frac{13}{4} $$$$ (x-2)^2+(y+2)^2 \leq \frac{41}{4} $$$$ (x-\frac{1}{2})^2+(y+1)^2 \leq \frac{5}{2}  $$$$ (x-1)^2+(y+2)^2 \leq  \frac{29}{4} $$$$ (x-\frac{1}{2})^2+(y+2)^2 \leq \frac{13}{2}  $$
1 reply
sqing
Jun 6, 2025
pooh123
3 hours ago
EGMO book YouTube tutorial
little-fermat   19
N Yesterday at 11:59 PM by Yiyj1
Source: EGMO book
Hey everyone,
Since EGMO (Euclidean Geometry for Mathematics Olympiad) by Evan Chen is a major resource for students preparing for Olympiad geometry, I have started (with Evan's permission) a YouTube tutorial in which I will explain the whole book chapter by chapter gradually.
The plan is to upload two videos for each chapter (Theory part and Practical part).
I am adding timestamps, so you can jump to the idea you want explaining on easily.
I might add other theory/examples outside the book, but the book is the main resource.
Currently Chapter 1: angle chasing theory part has been uploaded.
You can access the EGMO tutorial Here
Let me know if you have any suggestions either here on my discord server
Note: I have uploaded two tutorials Functional Equations and Inequality as well on the channel
[youtube]https://www.youtube.com/watch?v=8ZECzA4zb8c&t=2116s[/youtube]
19 replies
1 viewing
little-fermat
Oct 2, 2024
Yiyj1
Yesterday at 11:59 PM
KMO 2020 R1 P20
Tetra_scheme   1
N Yesterday at 11:23 PM by alexheinis
Call an ordered triple of positive integers $multiplicative$ if two terms of the triple multiply to the third. Find the number of permutations $f$ of the first $14$ positive integers to itself such that if


$(a,b,c)$ is a multiplicative triple, then $(f(a),f(b),f(c))$ is a multiplicative triple as well.
1 reply
Tetra_scheme
Yesterday at 3:36 PM
alexheinis
Yesterday at 11:23 PM
MAA messed up the order(n)
skipiano   203
N Yesterday at 9:53 PM by cxsmi
Source: 2017 USAJMO #1/USAMO #1
Prove that there are infinitely many distinct pairs $(a, b)$ of relatively prime integers $a>1$ and $b>1$ such that $a^b+b^a$ is divisible by $a+b$.
203 replies
skipiano
Apr 19, 2017
cxsmi
Yesterday at 9:53 PM
1987 AMC 12 #15 - Multiple Equations
dft   7
N Yesterday at 9:46 PM by mudkip42
If $(x, y)$ is a solution to the system
\[ xy=6 \qquad \text{and} \qquad x^2y+xy^2+x+y=63, \]
find $x^2+y^2.$

$ \textbf{(A)}\ 13 \qquad\textbf{(B)}\ \frac{1173}{32} \qquad\textbf{(C)}\ 55 \qquad\textbf{(D)}\ 69 \qquad\textbf{(E)}\ 81 $
7 replies
dft
Dec 31, 2011
mudkip42
Yesterday at 9:46 PM
1987 AMC 12 #14 - Angle in a Square
dft   4
N Yesterday at 9:45 PM by mudkip42
$ABCD$ is a square and $M$ and $N$ are the midpoints of $BC$ and $CD$ respectively. Then $\sin \theta=$
IMAGE
$ \textbf{(A)}\ \frac{\sqrt{5}}{5} \qquad\textbf{(B)}\ \frac{3}{5} \qquad\textbf{(C)}\ \frac{\sqrt{10}}{5} \qquad\textbf{(D)}\ \frac{4}{5} \qquad\textbf{(E)}\ \text{none of these} $
4 replies
dft
Dec 31, 2011
mudkip42
Yesterday at 9:45 PM
1987 AMC 12 #12 - Secretary's Letter
dft   2
N Yesterday at 9:41 PM by mudkip42
In an office, at various times during the day the boss gives the secretary a letter to type, each time putting the letter on top of the pile in the secretary's in-box. When there is time, the secretary takes the top letter off the pile and types it. If there are five letters in all, and the boss delivers them in the order $1\  2\  3\  4\  5$, which of the following could not be the order in which the secretary types them?

$ \textbf{(A)}\ 1\ 2\ 3\ 4\ 5  \qquad\textbf{(B)}\ 2\ 4\ 3\ 5\ 1 \qquad\textbf{(C)}\ 3\ 2\ 4\ 1\ 5 \qquad\textbf{(D)}\ 4\ 5\ 2\ 3\ 1 \\ \qquad\textbf{(E)}\ 5\ 4\ 3\ 2\ 1 $
2 replies
dft
Dec 31, 2011
mudkip42
Yesterday at 9:41 PM
1987 AMC 12 #11 - Simultaneous Equations
dft   2
N Yesterday at 9:39 PM by mudkip42
Let $c$ be a constant. The simultaneous equations
\begin{align*}
x-y = &\  2 \\
cx+y = &\  3 \\
\end{align*}
have a solution $(x, y)$ inside Quadrant I if and only if

$ \textbf{(A)}\ c=-1 \qquad\textbf{(B)}\ c>-1 \qquad\textbf{(C)}\ c<\frac{3}{2} \qquad\textbf{(D)}\ 0<c<\frac{3}{2}\\  \qquad\textbf{(E)}\ -1<c<\frac{3}{2} $
2 replies
dft
Dec 31, 2011
mudkip42
Yesterday at 9:39 PM
1987 AMC 12 #13 - Cardboard Tube
dft   4
N Yesterday at 9:37 PM by mudkip42
A long piece of paper $5$ cm wide is made into a roll for cash registers by wrapping it $600$ times around a cardboard tube of diameter $2$ cm, forming a roll $10$ cm in diameter. Approximate the length of the paper in meters. (Pretend the paper forms $600$ concentric circles with diameters evenly spaced from $2$ cm to $10$ cm.)

$ \textbf{(A)}\ 36\pi \qquad\textbf{(B)}\ 45\pi \qquad\textbf{(C)}\ 60\pi \qquad\textbf{(D)}\ 72\pi \qquad\textbf{(E)}\ 90\pi $
4 replies
dft
Dec 31, 2011
mudkip42
Yesterday at 9:37 PM
1987 AMC 12 #9 - Arithmetic Sequence
dft   3
N Yesterday at 9:21 PM by mudkip42
The first four terms of an arithmetic sequence are $a, x, b, 2x$. The ratio of $a$ to $b$ is

$ \textbf{(A)}\ \frac{1}{4} \qquad\textbf{(B)}\ \frac{1}{3} \qquad\textbf{(C)}\ \frac{1}{2} \qquad\textbf{(D)}\ \frac{2}{3} \qquad\textbf{(E)}\ 2 $
3 replies
dft
Dec 31, 2011
mudkip42
Yesterday at 9:21 PM
A VERY Long Bookshelf
DottedCaculator   65
N Yesterday at 9:21 PM by cxsmi
Let $n \geq 2$ be an integer. Carl has $n$ books arranged on a bookshelf. Each book has a height and a width. No two books have the same height, and no two books have the same width. Initially, the books are arranged in increasing order of height from left to right. In a move, Carl picks any two adjacent books where the left book is wider and shorter than the right book, and swaps their locations. Carl does this repeatedly until no further moves are possible. Prove that regardless of how Carl makes his moves, he must stop after a finite number of moves, and when he does stop, the books are sorted in increasing order of width from left to right.

Proposed by Milan Haiman
65 replies
DottedCaculator
Jun 21, 2020
cxsmi
Yesterday at 9:21 PM
1987 AMC 12 #10 - Ordered Triples
dft   2
N Yesterday at 9:03 PM by mudkip42
How many ordered triples $(a, b, c)$ of non-zero real numbers have the property that each number is the product of the other two?

$ \textbf{(A)}\ 1 \qquad\textbf{(B)}\ 2 \qquad\textbf{(C)}\ 3 \qquad\textbf{(D)}\ 4 \qquad\textbf{(E)}\ 5 $
2 replies
dft
Dec 31, 2011
mudkip42
Yesterday at 9:03 PM
a problem about cups
pzzd   3
N Jun 3, 2025 by vincentwant
Hello! I’m new to the AoPS forums, so apologies in advance if I’ve posted in the wrong place :-)

Here’s an interesting counting problem I’ve come up with that’s been bothering me for a while:

Say we have a tower of cups such that the top row has one cup, the row directly under that has two cups, the row under that has 3 cups, and so on such that every cup is supported by exactly two cups in the row under it. Each cup in the tower is labelled with a number or letter so that every cup is distinct. If a cup tower has $n$ rows, how many different ways can we pick up all the cups, starting at the top? (Assume that you can’t pick up a cup that’s under another cup, the tower would fall over.)
3 replies
pzzd
Jun 3, 2025
vincentwant
Jun 3, 2025
a problem about cups
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pzzd
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#1
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Hello! I’m new to the AoPS forums, so apologies in advance if I’ve posted in the wrong place :-)

Here’s an interesting counting problem I’ve come up with that’s been bothering me for a while:

Say we have a tower of cups such that the top row has one cup, the row directly under that has two cups, the row under that has 3 cups, and so on such that every cup is supported by exactly two cups in the row under it. Each cup in the tower is labelled with a number or letter so that every cup is distinct. If a cup tower has $n$ rows, how many different ways can we pick up all the cups, starting at the top? (Assume that you can’t pick up a cup that’s under another cup, the tower would fall over.)
This post has been edited 1 time. Last edited by pzzd, Jun 3, 2025, 7:14 PM
Reason: spelling mistake
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vincentwant
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This is equal to the number of Young tableaux of shape (n, n-1, ..., 1) which by the hook length formula is equal to $\frac{\binom{n+1}{2}!}{(2n-1)^1(2n-3)^2\dots(1)^n}$.
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pzzd
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ok, cool… but how do young tableaux apply to this problem exactly? this is a new concept for me haha
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vincentwant
1470 posts
#4 • 1 Y
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the condition for the tower not falling over is equivalent to this condition:
for each chain of cups, such that each cup is directly below the cup above it, the cups in the chain are removed from top to bottom.

one can quickly see that this is equivalent to each straight line of cups is removed from top to bottom, which is equivalent to the young tableaux condition
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