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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
2500 VIMC mathematics competition
OWOW   56
N 3 hours ago by sangriabeaver5
Hello! This is my second math competition I made up, this time, set in the year 2500 on a Venus base in the upper atmosphere.
This is basically AMC8 for Venusians.

2500 VIMC

What is the sum of all perfect squares less than 2500 in the form $9p^2$ where $p$ is prime?

Equilateral triangle $ABC$ has Area of $6$. If point $D$ is the midpoint of $AB$, then line $L$ is $CD$, which cuts the equilateral triangle in half. What is the sum of the perimeters of $ACD$ and $BCD$?

A Quadnumber is a number whose digits sum to $4$. How many positive 3-digit quadnumbers are there? (ex. $310$ is a quadnumber because it is positive, 3-digit, and the digits sum to $4$)

A wheel has $100$ equal sections with the numbers from $1$ to $100$ written on them. If you spin the wheel $N$ times, what is the probability that you will land on a prime number on any of the $N$ spins? (Clarification: Probability of Landing on a prime AT LEAST ONCE in the N spins)

Car A travels at a constant $10$ mph. Car B is a probabilistic car, and at the start of every hour, it gets the option for a $10\%$ chance of traveling at $5$ mph, an $80\%$ chance of traveling at $10$ mph, and a $10\%$ chance of traveling at $15$ mph. Once Car B decides on a speed, it acts like a normal car for the rest of the hour with a constant speed at which it picked at the start of the hour, and then the same options happen at the start of the next hour, and so on. Car A and Car B leave at the same time, and they both go in the same direction. What is the probability that Car B is right next to Car A (same speed, same position) for only $3$ hours in the next 6 hours?

If $x \equiv 2\pmod{3}$, and $x \equiv 3\pmod{4}$, and $x \equiv 4\pmod{5}$, what is the least positive value of $x$.

If $f(x)=3x-1$ and $g(x)$ is $x^2-3x+3$, what is $f(g(5)-f(4))+g(f(3)-g(2))+1$?



This competition is shorter than the Mars version (MIMC 2200) which was 10 questions. But this one I believe is harder than the MIMC. (designed to be, anyway) Btw here is the entire MIMC competition in case you missed it a couple weeks ago.



$25^2-10^2=$?

If ball A costs $\$1.50$, and ball B costs $\$1.75$, what is the average cost per ball if you buy $10$ of ball A and $4$ of ball B? Please write as an improper fraction

How many divisors does $2200^3$ have?

If $f(2200-k)=10(k-2)$, then what is $f(f(2^{11}))$?

If three distinct positive primes, $(p,q,r)$, sum to 50, what is the greatest possible value of $(r^p)-(q^p)$ such that $p<q<r$?

What positive integer $x$ satisfies: $x^5-(x+4)^3+10^{(5-3)}=0$?

If a circle with radius $1$ is inscribed in a square, which is inscribed in another circle, what is the area of the outer circle minus the area of the inner circle?

What is the sum of $b$ and $c$ such that the roots of $x^2+bx+c=0$ sum to $11c$ and multiply to $12b-7$?

If the operation $a\#b = \dfrac{(a-b+1)^2}{(b-a+1)^2}$, what is the largest possible value of $(3\#x)$ given that $x$ is a positive integer?

How many 4-digit numbers have the property that the sum of the thousands and tens digits combined is the square of the sum of the hundreds and ones digits combined?

Pls write all solutions like this:
ex. S1 (Contest: either VIMC or MIMC)
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Completed problems (I'm not going to show solutions here so other people can solve it)
MIMC: 1,2,3,4,5,6,7,8,9 (9/10 done)
VIMC: 1,3,4,6,7 (5/7 done)
56 replies
OWOW
Jul 16, 2025
sangriabeaver5
3 hours ago
Website to learn math
hawa   180
N Today at 2:17 AM by Inaaya
Hi, I'm kinda curious what website do yall use to learn math, like i dont find any website thats fun to learn math
180 replies
hawa
Apr 9, 2025
Inaaya
Today at 2:17 AM
9 MathCounts prep
ericheathclifffry   23
N Today at 2:13 AM by seabass17
Redacted
23 replies
ericheathclifffry
Jul 21, 2025
seabass17
Today at 2:13 AM
Goals for 2025-2026
Airbus320-214   407
N Today at 1:39 AM by Disjunction
Please write down your goal/goals for competitions here for 2025-2026.
407 replies
Airbus320-214
May 11, 2025
Disjunction
Today at 1:39 AM
9 Was this year's AMC 8 hard or easy
ChuMath   71
N Today at 1:16 AM by Leeoz
Question: Was this year's AMC 8 harder or easier than last year's (or the historical average)

71 replies
ChuMath
Jan 25, 2024
Leeoz
Today at 1:16 AM
FREE AMC 10 Bootcamp - Shine4Love Teens Club
mop   28
N Yesterday at 9:06 PM by mop
Hey everyone!

Want to get a head-start with AMC prep this year and bag that AIME qual/(D)HR this November? The Shine4Love Teens Club is excited to host a FREE 3 week long AMC 10 Bootcamp starting next Monday!

The course will cover fundamental concepts and problem-solving strategies for the AMC 10 in algebra, geometry, combinatorics, and number theory, providing the experience needed to give you the best shot at accomplishing your AMC goals!

Registration is completely free, although donations are open (all proceeds will be donated to charity!).

Date/Time:
4:00-6:00 p.m. PST on Mondays, Wednesdays, & Fridays

Format:
Classes will be held on Zoom, and class notes will be posted after each class on Google Classroom. Additional problem sets will be posted on Google Classroom for students to work on. The instructor's email will be open 24/7 for any questions!

Register/more details at tinyurl.com/amc10prepcourse

Hope to see you all soon!
28 replies
mop
Jul 15, 2025
mop
Yesterday at 9:06 PM
Perfect squares: 2011 USAJMO #1
v_Enhance   230
N Yesterday at 9:03 PM by Fly_into_the_sky
Find, with proof, all positive integers $n$ for which $2^n + 12^n + 2011^n$ is a perfect square.
230 replies
v_Enhance
Apr 28, 2011
Fly_into_the_sky
Yesterday at 9:03 PM
how to stay motivated
hgmium   22
N Yesterday at 6:28 PM by GeographyTutors
I'm finding prepping for AMC is feeling more and more boring each day (I just don't feel focused while doing problems and I'm always thinking of something else). I had a lot of motivation before, but now it just feels like a chore. Deep down, I still want to get DHR this year, I just don't know how to stay focused. Does anyone have any tips for locking in before it's too late? There's around three months left before AMC 10.
22 replies
hgmium
Jul 20, 2025
GeographyTutors
Yesterday at 6:28 PM
Quadrilateral Inscribed in Semicircle
djmathman   59
N Yesterday at 5:44 PM by Kempu33334
Source: 2013 USAJMO #5
Quadrilateral $XABY$ is inscribed in the semicircle $\omega$ with diameter $XY$. Segments $AY$ and $BX$ meet at $P$. Point $Z$ is the foot of the perpendicular from $P$ to line $XY$. Point $C$ lies on $\omega$ such that line $XC$ is perpendicular to line $AZ$. Let $Q$ be the intersection of segments $AY$ and $XC$. Prove that \[\dfrac{BY}{XP}+\dfrac{CY}{XQ}=\dfrac{AY}{AX}.\]
59 replies
djmathman
May 1, 2013
Kempu33334
Yesterday at 5:44 PM
2019 CIME I/14 moment
r00tsOfUnity   42
N Yesterday at 3:47 PM by mudkip42
Source: 2024 AIME II #10
Let $\triangle ABC$ have circumcenter $O$ and incenter $I$ with $\overline{IA}\perp\overline{OI}$, circumradius $13$, and inradius $6$. Find $AB\cdot AC$.
42 replies
r00tsOfUnity
Feb 8, 2024
mudkip42
Yesterday at 3:47 PM
Does anyone have access to the current AMM edition? I’d like to check out the pr
Khalifakhalifa   1
N Yesterday at 4:36 AM by Khalifakhalifa
Does anyone have access to the current AMM edition? I’d like to check out the problems section.
1 reply
Khalifakhalifa
Tuesday at 11:15 AM
Khalifakhalifa
Yesterday at 4:36 AM
Improving timing on AMC 10
AdrienMarieLegendre   20
N Yesterday at 3:48 AM by ahxun2006
hello,
I'm currently preparing for the AMC 10, but I'm struggling with time. When doing past tests, I can only answer 10-12 questions in the 75-minute time frame. I can solve the rest of the questions, but they take me fairly long to complete (15-30 mins depending on the question). Do you guys have any tips/strategies on improving timing? Would it be best just to solve more problems?
20 replies
AdrienMarieLegendre
Jul 16, 2025
ahxun2006
Yesterday at 3:48 AM
Stressed spelled backwards
centslordm   27
N Yesterday at 3:38 AM by W33
Source: AIME 2025 #3
The 9 members of a baseball team went to an ice-cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by $1000.$
27 replies
centslordm
Feb 7, 2025
W33
Yesterday at 3:38 AM
Research Advice?
AdrienMarieLegendre   8
N Yesterday at 12:38 AM by sadas123
Does anyone have any advice on reading research papers? I wanna go through some so I could potentially start a project later this yr, but I don't know how it'd be best to read papers (for reference, I wanna do quantum computing). Should I just go through the abstract and introduction and then read the results without reading much of the middle? What should I do about advanced terminology for which I don't have enough theory to understand? Also, to anyone who's done a project, is it necessary to work on it with a professor during the summer or is it possible to contact someone during the school year too?

note: sorry if this is kinda off topic for this forum
8 replies
AdrienMarieLegendre
Jul 21, 2025
sadas123
Yesterday at 12:38 AM
An annoying math problem
Wolfpierce   10
N Jun 5, 2025 by Capybara7017
Okay so what is 2/((√3+1)((3 to the 1/4)+1)((3 to the 1/8)+1)((3 to the 1/16)+1)) to the power of 32?
10 replies
Wolfpierce
Jun 5, 2025
Capybara7017
Jun 5, 2025
An annoying math problem
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Wolfpierce
37 posts
#1
Y by
Okay so what is 2/((√3+1)((3 to the 1/4)+1)((3 to the 1/8)+1)((3 to the 1/16)+1)) to the power of 32?
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pingpongmerrily
4055 posts
#2
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Could somebody put that in latex I'm too lazy sob
i can't really read that rn but if its in latex i can solve it for you lol
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Capybara7017
682 posts
#3
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$\left( \frac{2}{\left(\sqrt{3} + 1\right) \left(3^{1/4} + 1\right) \left(3^{1/8} + 1\right) \left(3^{1/16} + 1\right)} \right)^{32}$

ur welcome
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juliarwu
283 posts
#4
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lol sniped :rotfl:
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Wolfpierce
37 posts
#5
Y by
Sorry don't know all the keyboard shortcuts
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elizhang101412
1371 posts
#6
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div by 3^1/16-1 then the exp becomes 1^32=1, so it is 1*(3^1/16-1) which doesn't have a clean answer
edit: i've done an extreme dumb here that somehow gives the 32nd root but it still isn't a nice answer i think
This post has been edited 3 times. Last edited by elizhang101412, Jun 5, 2025, 2:26 AM
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Wolfpierce
37 posts
#7
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Well I do know in google docs
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golden_star_123
223 posts
#8
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Consider the interior of the parentheses. Multiply by $\frac{\sqrt[16]3 - 1}{\sqrt[16]3 - 1}$,

we obtain $$\frac{2(\sqrt[16]3 - 1)}{(\sqrt 3 + 1) (\sqrt[4]3 + 1)(\sqrt[8]3 + 1)(\sqrt[8]3 - 1)} $$
The denominator telescope by difference of squares, and the expression because $\sqrt[16]3 -1$.

Taking this to the power of $32$, our answer is $(\sqrt[16]3 - 1)^{32}$,

which does not have a clean expansion.
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Soupboy0
633 posts
#9
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umm approximately 0
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Yihangzh
1546 posts
#10
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My answer, I dont think its correct
This post has been edited 1 time. Last edited by Yihangzh, Jun 5, 2025, 4:57 AM
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Capybara7017
682 posts
#11
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im not smart but I think u can use difference of squares to individually cancel each of the bottom terms
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