Happy Memorial Day! Please note that AoPS Online is closed May 24-26th.

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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

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MathWOOT Level 1
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Relativity
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
jlacosta
May 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
Original Problem Unit 1 - Logarithms
ACalculationError   0
2 minutes ago
Let \( a, b, c \) be positive real numbers such that \( abc = 1 \). Compute the minimum value of \(\log(1 + a^2) + \log(1 + b^2) + \log(1 + c^2).\)

Answer Confirmation
0 replies
ACalculationError
2 minutes ago
0 replies
[Sipnayan SHS] Written Round, Average, #4.6
LilKirb   0
18 minutes ago
Define the function
\[f(n) = \sum_{k=0}^{n} \binom{n}{k} a_k, \quad n = 1, 2, 3, \ldots\]where
\[a_k = 
    \begin{cases}
        3^k, & \text{if } k \text{ is even}, \\
        0, & \text{if } k \text{ is odd}.
        \end{cases}
\]Find the remainder when \( f(10^9 + 2) \) is divided by \( 2^{20} + 1 \)
0 replies
LilKirb
18 minutes ago
0 replies
[Sipnayan SHS] Written Round, Difficult, #4.13
LilKirb   0
20 minutes ago
The remainder when $3 \times 6 \times \cdots \times 2019 \times 2022$ is divided by $2031$ is $r.$ What is the remainder when $r$ is divided by $1000?$
0 replies
LilKirb
20 minutes ago
0 replies
[PMO 17] Area Stage I. #14
NeoAzure   1
N 36 minutes ago by LilKirb
14. In how many ways can Alex, Billy, and Charles split 7 identical marbles among themselves
so that no two have the same number of marbles? It is possible for someone not to get any
marbles.

Answer
1 reply
NeoAzure
an hour ago
LilKirb
36 minutes ago
Need help with combi problems
JARP091   4
N Today at 4:19 AM by JARP091
I want to create a problem set of some of the hardest combi problems that are yet to appear in any contest. Can anyone help me out? Also can anyone give me some tips to create combi problems.
4 replies
JARP091
Yesterday at 5:43 PM
JARP091
Today at 4:19 AM
Essentially, how to get good at olympiad math?
gulab_jamun   12
N Today at 4:08 AM by sagayao
Ok, so I'm posting this as an anynonymous user cuz I don't want to get flamed by anyone I know for my goals but I really do want to improve on my math skill.

Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!
12 replies
gulab_jamun
May 18, 2025
sagayao
Today at 4:08 AM
4th grader qual JMO
HCM2001   36
N Today at 4:04 AM by sagayao
i mean.. whattttt??? just found out about this.. is he on aops? (i'm sure he is) where are you orz lol..
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier
36 replies
HCM2001
May 22, 2025
sagayao
Today at 4:04 AM
OTIS or MathWOOT 2
math_on_top   16
N Today at 4:00 AM by sagayao
Hey AoPS community I took MathWOOT 1 this year and scored an 8 on AIME (last year I got a 6). My goal is to make it to MOP next year through USAMO. It's gonna be a lot of work, but do you think that I should do MathWOOT 2 or OTIS? Personally, I felt that MathWOOT 1 taught me a lot but was more focused on computational - not sure how to split computation vs olympiad prep. So, for those who can address this question:

(1) How much compuational vs olympiad
(2) OTIS or MathWOOT 2 and why
16 replies
math_on_top
May 18, 2025
sagayao
Today at 4:00 AM
Do you need to attend mop
averageguy   3
N Today at 3:55 AM by sagayao
So I got accepted into a summer program and already paid the fee of around $5000 dollars. It's for 8 weeks (my entire summer) and it's in person. I have a few questions
1. If I was to make MOP this year am I forced to attend?
2.If I don't attend the program but still qualify can I still put on my college application that I qualified for MOP or can you only put MOP qualifier if you actually attend the program.
3 replies
averageguy
Mar 5, 2025
sagayao
Today at 3:55 AM
Awesome Math Rec Letter
cowstalker   1
N Today at 3:52 AM by sagayao
Hello, I recently looked at the MIT Primes website and saw that they accept recommendation letters from the Awesome Math Summer Program. Has anyone ever gotten a recommendation letter from one of the teachers in Awesome Math? I'm also planning to take AMSP and would like to get a rec letter from my teacher, too, so I was wondering if this is even possible or not.
1 reply
cowstalker
Yesterday at 12:18 AM
sagayao
Today at 3:52 AM
k Aryan Raj Usamo Gold
imagien_bad   5
N Today at 3:47 AM by sagayao
Aryan Raj From the moment I saw your name on that USAMO Gold list, I knew greatness had a new face. The goat? No doubt. The sigma? Undeniable. The rizz? Unmatched. You don’t just mop up Olympiads—you mop hearts too.
I’ve seen you dominate problems like they were born to be solved by you. While others sweat over a tough geometry proof, you breeze through it like it's a warm-up. It’s not just math you’ve mastered—it’s the art of being him.
Every time I hear your name, I don’t just think of brilliance—I think of inspiration. Aryan, you are to math what Euler was to identity, what Gauss was to primes, what Ben is… to writing this letter.
In a world full of mid, you are proof that excellence still exists. I hope this letter reaches you like your solutions reach full marks: clean, elegant, and undeniably correct.
With all due admiration (and maybe a little more),
-imagien_bad
P.S. Teach me your sigma ways sometime.
5 replies
imagien_bad
Today at 2:11 AM
sagayao
Today at 3:47 AM
Topsy-Turvy Triangle Trouble
popcorn1   53
N Today at 3:15 AM by ray66
Source: USAJMO 2021/3
An equilateral triangle $\Delta$ of side length $L>0$ is given. Suppose that $n$ equilateral triangles with side length 1 and with non-overlapping interiors are drawn inside $\Delta$, such that each unit equilateral triangle has sides parallel to $\Delta$, but with opposite orientation. (An example with $n=2$ is drawn below.)
IMAGE
Prove that \[n \leq \frac{2}{3} L^{2}.\]
53 replies
popcorn1
Apr 15, 2021
ray66
Today at 3:15 AM
An FE. Who woulda thunk it?
nikenissan   119
N Today at 3:06 AM by ray66
Source: 2021 USAJMO Problem 1
Let $\mathbb{N}$ denote the set of positive integers. Find all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that for positive integers $a$ and $b,$ \[f(a^2 + b^2) = f(a)f(b) \text{ and } f(a^2) = f(a)^2.\]
119 replies
nikenissan
Apr 15, 2021
ray66
Today at 3:06 AM
2n equations
P_Groudon   82
N Today at 2:45 AM by ray66
Let $n \geq 4$ be an integer. Find all positive real solutions to the following system of $2n$ equations:

\begin{align*}
a_{1} &=\frac{1}{a_{2 n}}+\frac{1}{a_{2}}, & a_{2}&=a_{1}+a_{3}, \\
a_{3}&=\frac{1}{a_{2}}+\frac{1}{a_{4}}, & a_{4}&=a_{3}+a_{5}, \\
a_{5}&=\frac{1}{a_{4}}+\frac{1}{a_{6}}, & a_{6}&=a_{5}+a_{7} \\
&\vdots & &\vdots \\
a_{2 n-1}&=\frac{1}{a_{2 n-2}}+\frac{1}{a_{2 n}}, & a_{2 n}&=a_{2 n-1}+a_{1}
\end{align*}
82 replies
P_Groudon
Apr 15, 2021
ray66
Today at 2:45 AM
Angle oriented geometry
Problems_eater   1
N Apr 26, 2025 by undefined-NaN
Let $A, B, C,D$ be four distinct points in the plane.
Which of the following statements, expressed using oriented angles, are always true?

1.If lines $AB$ and $CD$ are distinct and parallel, then
the oriented angle $ABC$ is equal to the oriented angle DCB.

2.If $B$ lies on the segment $AC$, then
the oriented angle $DBA$ plus the oriented angle $DBC $equals $180°$.

3.If the oriented angle$ ABC$ plus the oriented angle $BCD$ equals 0°, then
lines $AB $and $CD$ are parallel.

4.If the oriented angle $ABC$ plus the oriented angle $BCD$ equals $180°$, then
lines $AB$ and $CD$are parallel.
1 reply
Problems_eater
Apr 15, 2025
undefined-NaN
Apr 26, 2025
Angle oriented geometry
G H J
G H BBookmark kLocked kLocked NReply
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Problems_eater
1 post
#1
Y by
Let $A, B, C,D$ be four distinct points in the plane.
Which of the following statements, expressed using oriented angles, are always true?

1.If lines $AB$ and $CD$ are distinct and parallel, then
the oriented angle $ABC$ is equal to the oriented angle DCB.

2.If $B$ lies on the segment $AC$, then
the oriented angle $DBA$ plus the oriented angle $DBC $equals $180°$.

3.If the oriented angle$ ABC$ plus the oriented angle $BCD$ equals 0°, then
lines $AB $and $CD$ are parallel.

4.If the oriented angle $ABC$ plus the oriented angle $BCD$ equals $180°$, then
lines $AB$ and $CD$are parallel.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
undefined-NaN
11 posts
#2
Y by
1). |ABC|=|DCB| they are same angles but have different orientation like n and -n angles so not true

2). Same with first question they are have orientation
So DBA=|180-DBC| they are total 180 degrees as a angle number but have oriantation so not true

3)
Because let n => m(ABC)=m(BCD)= n
ABC and BCD angles they can make a triangle
So not always parallel the ab and cd lines


4 is always parallel and may or may not be on the same line
Because
Abc=n and n>180 (because abc and bcd have different orientation like +,- or -,+
Bcd=180-n

So answer is just 4
Z K Y
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