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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/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
Mar 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
Warm-up combinatorics
giangtruong13   1
N 2 minutes ago by mathprodigy2011
On a square board, in every squares they fill in with all sign $+$. Then, perform the sign change progress ( from sign $+$ to sign $-$, from sign $-$ to sign $+$)follow these steps in turn:
- $Step 1$: signs in all squares on the line $i$ will be changed $i$ times,$ i= 1,2,3,…,2019$
- $ Step 2$: Signs in all squares on the column $j$ will be changed $3j+1$ times, $j=1,2,3,..2019$
Find all the remaining signs on the board after performing the above progress.
1 reply
giangtruong13
21 minutes ago
mathprodigy2011
2 minutes ago
Inequalities
sqing   0
an hour ago
Let $ a,b,c\geq 2  . $ Prove that
$$(a-1)(b^2-2)(c-1) -  \frac{1}{2}abc\geq -2$$$$(a^2-2)(b-1)(c^2-2) - \frac{3}{2}abc\geq -6$$
0 replies
sqing
an hour ago
0 replies
one intersting
teomihai   3
N an hour ago by hexuhdecimal
Let $n $ it is fixed positiv number.
Find $card\{(x,y) | |x|+|y|<n \}$, where $x,y$ are integer numbers .
3 replies
teomihai
Mar 15, 2025
hexuhdecimal
an hour ago
Discrete problem
ThanhNg   1
N 2 hours ago by RPCX
Prove that : From any 161 natural numbers, we can always find 81 numbers whose sum is divisible by 81.
1 reply
ThanhNg
Yesterday at 4:23 PM
RPCX
2 hours ago
Does anyone see USAJMO on their portal
averageguy   3
N Today at 4:41 AM by MathRook7817
On my portal underneath "competition available to be taken" I see nothing there even though I'm supposed to take the USAJMO tomorrow. Does anyone else see USA(J)MO underneath there. Is it supposed to appear there only tomorrow.
3 replies
averageguy
Today at 3:13 AM
MathRook7817
Today at 4:41 AM
Evan's mean blackboard game
hwl0304   71
N Today at 3:24 AM by quantam13
Source: 2019 USAMO Problem 5, 2019 USAJMO Problem 6
Two rational numbers \(\tfrac{m}{n}\) and \(\tfrac{n}{m}\) are written on a blackboard, where \(m\) and \(n\) are relatively prime positive integers. At any point, Evan may pick two of the numbers \(x\) and \(y\) written on the board and write either their arithmetic mean \(\tfrac{x+y}{2}\) or their harmonic mean \(\tfrac{2xy}{x+y}\) on the board as well. Find all pairs \((m,n)\) such that Evan can write 1 on the board in finitely many steps.

Proposed by Yannick Yao
71 replies
hwl0304
Apr 18, 2019
quantam13
Today at 3:24 AM
Convolution of order f(n)
trumpeter   75
N Today at 3:04 AM by quantam13
Source: 2019 USAMO Problem 1
Let $\mathbb{N}$ be the set of positive integers. A function $f:\mathbb{N}\to\mathbb{N}$ satisfies the equation \[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]for all positive integers $n$. Given this information, determine all possible values of $f(1000)$.

Proposed by Evan Chen
75 replies
1 viewing
trumpeter
Apr 17, 2019
quantam13
Today at 3:04 AM
AMC 12 Question
sadas123   12
N Today at 2:50 AM by jb2015007
Hello! I am a 6th grader this year about to become 7th grade next year. I was wondering if I should take the AMC 12 next year because I think I am ready for it, I was thinking to do AMC 10 A and AMC 12 B, do you think it is a good idea? Here are the courses I finished and now I am working on:

Finished:
1. Intro Algebra
2. Intro Number Theory
3. Intro Counting and Probability
4. Volume 1

Working on:
1. Intermdiate Counting and Probability
2. Three Year Mathcounts Marathon

Upcoming:
1. Intro Geomtery (Next Month)
2. Intro to Alg (May)
3. Pre-calc (Summer)
4. Volume 2???

Stats for AMC 12 (Mocked):

1. AMC 12 A 2024: 100.5
2. AMC 12 B 2024: 105
3. AMC 12 A 2023: 96

The reason why I sometimes I get 100+ is because sometimes I know how to do the first step of the problem but the last step I have to kind of infrence but still i know how to do the problem.
12 replies
sadas123
Yesterday at 5:11 PM
jb2015007
Today at 2:50 AM
Day Before Tips
elasticwealth   20
N Today at 2:44 AM by KevinYang2.71
Hi Everyone,

USA(J)MO is tomorrow. I am a Junior, so this is my last chance. I made USAMO by ZERO points but I've actually been studying oly seriously since JMO last year. I am more stressed than I was before AMC/AIME because I feel Olympiad is more unpredictable and harder to prepare for. I am fairly confident in my ability to solve 1/4 but whether I can solve the rest really leans on the topic distribution.

Anyway, I'm just super stressed and not sure what to do. All tips are welcome!

Thanks everyone! Good luck tomorrow!
20 replies
elasticwealth
Today at 12:09 AM
KevinYang2.71
Today at 2:44 AM
Prove Collinearity
tc1729   126
N Today at 2:05 AM by quantam13
Source: 2012 USAMO Day 2 #5 and USAJMO Day 2 #6
Let $P$ be a point in the plane of $\triangle ABC$, and $\gamma$ a line passing through $P$. Let $A', B', C'$ be the points where the reflections of lines $PA, PB, PC$ with respect to $\gamma$ intersect lines $BC, AC, AB$ respectively. Prove that $A', B', C'$ are collinear.
126 replies
tc1729
Apr 25, 2012
quantam13
Today at 2:05 AM
10B Score Thread
BS2012   140
N Today at 1:17 AM by hashbrown2009
$\begin{tabular}{c|c|c|c|c}Username & Grade & 10B \\ \hline
BS2012 & 9 & 144  \\
\end{tabular}$
EDIT: I found out i didn't silly #19, so i got 144
140 replies
BS2012
Nov 13, 2024
hashbrown2009
Today at 1:17 AM
ABMC 2025 IN-PERSON Contest (April 5th)
ilovepizza2020   7
N Today at 12:50 AM by MagicPotato
The 9th annual Acton-Boxborough Math Competition (ABMC) is quickly approaching! This year's ABMC will be held in-person at RJ Grey Junior High School, Acton, MA, on April 5th, 2025. The competition includes individual rounds and a team round, in which teams of 2-4 students participate. Anyone in grade 8 or below is welcome! You must register to compete. For more information about registration and the tentative schedule, please consult our website: https://abmathcompetitions.org/2025-contest/.

We offer prizes not only to top competitors; several of our sponsor prizes and educational awards are raffled among all in-person participants. Additionally, there are separate prizes for the top-scoring elementary schoolers.


For more information, visit https://abmathcompetitions.org/, especially the 2025 Competition page.
For the mailing list, visit https://abmathcompetitions.org/contact/.

Best,
ABMC Coordinators
7 replies
ilovepizza2020
Mar 16, 2025
MagicPotato
Today at 12:50 AM
Tennessee Math Tournament (TMT) Online 2025
TennesseeMathTournament   32
N Today at 12:13 AM by TennesseeMathTournament
Hello everyone! We are excited to announce a new competition, the Tennessee Math Tournament, created by the Tennessee Math Coalition! Anyone can participate in the virtual competition for free.

The testing window is from March 22nd to April 5th, 2025. Virtual competitors may participate in the competition at any time during that window.

The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.

To register and see more information, click here!

If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!
32 replies
TennesseeMathTournament
Mar 9, 2025
TennesseeMathTournament
Today at 12:13 AM
Burnout?
xHypotenuse   5
N Yesterday at 11:42 PM by xHypotenuse
Hello everyone, these days I have a burning urge to pick up new math concepts because I think they are important/interesting. But I also feel a constant burnout where I get really tired when I try to solve math problems of these new concepts. I can't and then it gets very demotivating. I don't want to take a break from math because solving problems have become such a natural part of me and also I really want to qualify for usamo next year (my last year I can since it's senior yr). Any suggestions?
5 replies
1 viewing
xHypotenuse
Yesterday at 7:32 PM
xHypotenuse
Yesterday at 11:42 PM
PHP + Fibonacci
SomeonecoolLovesMaths   5
N Mar 16, 2025 by OronSH
The Question

I have tried to search this problem both inside/outside AoPS but was unable to find a solution, specifically with the use of PHP in it. It would be really helpful if someone posted a solution to it.
5 replies
SomeonecoolLovesMaths
Mar 15, 2025
OronSH
Mar 16, 2025
PHP + Fibonacci
G H J
G H BBookmark kLocked kLocked NReply
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SomeonecoolLovesMaths
3141 posts
#1
Y by
The Question

I have tried to search this problem both inside/outside AoPS but was unable to find a solution, specifically with the use of PHP in it. It would be really helpful if someone posted a solution to it.
Z K Y
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RoyalPrince
134 posts
#2
Y by
  There exists a Fibonacci number \(F_{n}\) that ends with 2007 zeros. But I can't find what number it is if that's what you're looking for
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SomeonecoolLovesMaths
3141 posts
#3
Y by
RoyalPrince wrote:
There exists a Fibonacci number \(F_{n}\) that ends with 2007 zeros. But I can't find what number it is if that's what you're looking for

No not really that. I am looking for a proof for the existence of such a number.
Z K Y
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SomeonecoolLovesMaths
3141 posts
#4
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I would also love it if you guys could help me with this.

Let $a_1, a_2, \ldots, a_{20}$ be distinct positive integers not exceeding $70$. Show that there is some $k$ so that $a_i - a_j = k$ for four different pairs $(i, j)$.
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mathprodigy2011
224 posts
#5
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SomeonecoolLovesMaths wrote:
The Question

I have tried to search this problem both inside/outside AoPS but was unable to find a solution, specifically with the use of PHP in it. It would be really helpful if someone posted a solution to it.

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OronSH
1720 posts
#6
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For any $k$ the sequence $F_n\pmod k$ is periodic, since there are finitely many possible pairs $(F_n,F_{n+1})$ so eventually one will repeat. Additionally since $F_n,F_{n+1}$ uniquely determine $F_{n-1}$ the sequence is purely periodic. Since $F_0=F_2-F_1=0$ there is some other $n$ with $F_n\equiv 0\pmod k$. Then take $k=10^{2007}$
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