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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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
Apr 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
weird permutation problem
Sedro   3
N 43 minutes ago by Sedro
Let $\sigma$ be a permutation of $1,2,3,4,5,6,7$ such that there are exactly $7$ ordered pairs of integers $(a,b)$ satisfying $1\le a < b \le 7$ and $\sigma(a) < \sigma(b)$. How many possible $\sigma$ exist?
3 replies
Sedro
Yesterday at 2:09 AM
Sedro
43 minutes ago
Vieta's Bash (I think??)
Sid-darth-vater   7
N an hour ago by vanstraelen
I technically have a solution (I didn't come up with it, it was the official solution) but it seems unintuitive. Can someone find a sol/explain to me how they got to it? (like why did u do the steps that u did) sorry if this seems a lil vague

7 replies
Sid-darth-vater
3 hours ago
vanstraelen
an hour ago
MathILy 2025 Decisions Thread
mysterynotfound   6
N 2 hours ago by BossLu99
Discuss your decisions here!
also share any relevant details about your decisions if you want
6 replies
+1 w
mysterynotfound
Today at 3:35 AM
BossLu99
2 hours ago
2025 USA IMO
john0512   81
N 2 hours ago by BossLu99
Congratulations to all of you!!!!!!!

Alexander Wang
Hannah Fox
Karn Chutinan
Andrew Lin
Calvin Wang
Tiger Zhang

Good luck in Australia!
81 replies
john0512
Apr 19, 2025
BossLu99
2 hours ago
A problem involving modulus from JEE coaching
AshAuktober   6
N 2 hours ago by no_room_for_error
Solve over $\mathbb{R}$:
$$|x-1|+|x+2| = 3x.$$
(There are two ways to do this, one being bashing out cases. Try to find the other.)
6 replies
AshAuktober
Today at 8:44 AM
no_room_for_error
2 hours ago
Combinatorial proof
MathBot101101   9
N 2 hours ago by MathBot101101
Is there a way to prove
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}=1-\frac{1}{{n+1)!}
without induction and using only combinatorial arguments?

Induction proof wasn't quite as pleasing for me.
9 replies
MathBot101101
Yesterday at 7:37 AM
MathBot101101
2 hours ago
k VOLUNTEERING OPPORTUNITY OPEN TO HIGH/MIDDLE SCHOOLERS
im_space_cadet   1
N 2 hours ago by elasticwealth
Hi everyone!
Do you specialize in contest math? Do you have a passion for teaching? Do you want to help leverage those college apps? Well, I have something for all of you.

I am im_space_cadet, and during the fall of last year, I opened my non-profit DeltaMathPrep which teaches students preparing for contest math the problem-solving skills they need in order to succeed at these competitions. Currently, we are very much understaffed and would greatly appreciate the help of more tutors on our platform.

Each week on Saturday and Wednesday, we meet once for each competition: Wednesday for AMC 8 and Saturday for AMC 10 and we go over a past year paper for the entire class. On both of these days, we meet at 9PM EST in the night.

This is a great opportunity for anyone who is looking to have a solid activity to add to their college resumes that requires low effort from tutors and is very flexible with regards to time.

This is the link to our non-profit for anyone who would like to view our initiative:
https://www.deltamathprep.org/

If you are interested in this opportunity, please send me a DM on AoPS or respond to this post expressing your interest. I look forward to having you all on the team!

Thanks,
im_space_cadet
1 reply
im_space_cadet
3 hours ago
elasticwealth
2 hours ago
2025 PROMYS Results
Danielzh   28
N 3 hours ago by ConfidentKoala4
Discuss your results here!
28 replies
Danielzh
Apr 18, 2025
ConfidentKoala4
3 hours ago
LMT Spring 2025 and Girls' LMT 2025
vrondoS   30
N 3 hours ago by Mintylemon66
The Lexington High School Math Team is proud to announce LMT Spring 2025 and our inaugural Girls’ LMT 2025! LMT is a competition for middle school students interested in math. Students can participate individually, or on teams of 4-6 members. This announcement contains information for BOTH competitions.

LMT Spring 2025 will take place from 8:30 AM-5:00 PM on Saturday, May 3rd at Lexington High School, 251 Waltham St., Lexington, MA 02421.

The competition will include two individual rounds, a Team Round, and a Guts Round, with a break for lunch and mini-events. A detailed schedule is available at https://lhsmath.org/LMT/Schedule.

There is a $15 fee per participant, paid on the day of the competition. Pizza will be provided for lunch, at no additional cost.

Register for LMT at https://lhsmath.org/LMT/Registration/Home.

Girls’ LMT 2025 will be held ONLINE on MathDash from 11:00 AM-4:15 PM EST on Saturday, April 19th, 2025. Participation is open to middle school students who identify as female or non-binary. The competition will include an individual round and a team round with a break for lunch and mini-events. It is free to participate.

Register for GLMT at https://www.lhsmath.org/LMT/Girls_LMT.

More information is available on our website: https://lhsmath.org/LMT/Home. Email lmt.lhsmath@gmail.com with any questions.
30 replies
vrondoS
Mar 27, 2025
Mintylemon66
3 hours ago
What's the easiest proof-based math competition?
Muu9   1
N 4 hours ago by EaZ_Shadow
In terms of the difficulty of the questions, not the level of competition. There's USAJMO, but surely there must be countries with less developed competitive math scenes whose Olympiads are easier.
1 reply
Muu9
4 hours ago
EaZ_Shadow
4 hours ago
Discuss the Stanford Math Tournament Here
Aaronjudgeisgoat   284
N 5 hours ago by KevinChen_Yay
I believe discussion is allowed after yesterday at midnight, correct?
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag

Answers for the Algebra Subject Test
Estimated Algebra Cutoffs
Answers for the Geometry Subject Test
Estimated Geo Cutoffs
Answers for the Discrete Subject Test
Estimated Cutoffs for Discrete
Answers for the Team Round
Guts Answers
284 replies
Aaronjudgeisgoat
Apr 14, 2025
KevinChen_Yay
5 hours ago
2021 AMC 12A #25
franzliszt   27
N Today at 6:53 AM by Magnetoninja
Source: 2021 AMC 12A #25
Let $d(n)$ denote the number of positive integers that divide $n$, including $1$ and $n$. For example, $d(1)=1,d(2)=2,$ and $d(12)=6$. (This function is known as the divisor function.) Let \[f(n)=\frac{d(n)}{\sqrt[3]{n}}.\]There is a unique positive integer $N$ such that $f(N)>f(n)$ for all positive integers $n\ne N$. What is the sum of the digits of $N?$

$\textbf{(A) }5 \qquad \textbf{(B) }6 \qquad \textbf{(C) }7 \qquad \textbf{(D) }8\qquad \textbf{(E) }9$
27 replies
1 viewing
franzliszt
Feb 5, 2021
Magnetoninja
Today at 6:53 AM
How many people get waitlisted st promys?
dragoon   24
N Today at 4:33 AM by freshestcheese
Asking for a friend here
24 replies
dragoon
Apr 18, 2025
freshestcheese
Today at 4:33 AM
Deciding between Ross and HCSSiM
akliu   27
N Today at 3:01 AM by scinderella220
Hey! I got accepted into Ross Indiana, and I think I'll probably also get accepted into HCSSiM. I've been looking between the two camps, and I'm trying to decide which one to go to -- both seem like really fun options.

Instead of trying to explain my personal preferences and thought processes, I thought it might be a good idea to ask the community for their personal opinions on these camps. What are some things that you like or dislike about both camps? (Whether it be through personal experience or by word-of-mouth, but please specify if it's just something you've heard)

This will probably help me be more informed on making a final decision, so I'd appreciate any advice. Thanks in advance!
27 replies
akliu
Apr 18, 2025
scinderella220
Today at 3:01 AM
Real variables inequality
JK1603JK   1
N Apr 3, 2025 by lbh_qys
Let a,b,c\in R then prove that \frac{15}{2}\cdot\frac{a^2+b^2+c^2}{(a+b+c)^2}+\frac{ab}{a^2+b^2}+\frac{bc}{b^2+c^2}+\frac{ca}{c^2+a^2}\ge 4
1 reply
JK1603JK
Apr 3, 2025
lbh_qys
Apr 3, 2025
Real variables inequality
G H J
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JK1603JK
49 posts
#1
Y by
Let a,b,c\in R then prove that \frac{15}{2}\cdot\frac{a^2+b^2+c^2}{(a+b+c)^2}+\frac{ab}{a^2+b^2}+\frac{bc}{b^2+c^2}+\frac{ca}{c^2+a^2}\ge 4
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lbh_qys
544 posts
#2
Y by
JK1603JK wrote:
Let $a,b,c\in \mathbb{R}$ and $a+b+c \neq 0$ then prove that $$\frac{15}{2}\cdot\frac{a^2+b^2+c^2}{(a+b+c)^2}+\frac{ab}{a^2+b^2}+\frac{bc}{b^2+c^2}+\frac{ca}{c^2+a^2}\ge 4$$

WLOG \(a+b+c=5\). Then the original inequality is equivalent to
\[
15\sum \frac{a^2}{5^2}+\sum \frac{2ab}{a^2+b^2}=15\sum \frac{a^2}{\left(\sum a\right)^2}+\sum \frac{(a+b)^2}{a^2+b^2}-3\geq 8,
\]that is,
\[
3\sum \frac{a^2}{5}+\sum \frac{(a+b)^2}{a^2+b^2}\geq 11.
\]
Let
\[
x=2-a,\quad y=2-b,\quad z=2-c,
\]so that
\[
x+y+z=1.
\]Define
\[
q=xy+yz+zx \quad \text{and} \quad r=xyz.
\]Then the inequality is equivalent to proving
\[
3\sum \frac{(2-x)^2}{5}+\sum \frac{(4-x-y)^2}{(2-x)^2+(2-y)^2}\geq 11.
\]
According to the Cauchy--Schwarz inequality,
\[
\sum \frac{(4-x-y)^2}{(2-x)^2+(2-y)^2}\geq \frac{\left(\sum (4-x-y)(6-z)\right)^2}{\sum \left[(2-x)^2+(2-y)^2\right](6-z)^2}.
\]
Since
\[
\sum (2-x)^2=9-2q,
\]\[
\sum (4-x-y)(6-z)=56+2q,
\]\[
\sum \left[(2-x)^2+(2-y)^2\right](6-z)^2=560-80q+2q^2+44r,
\]it suffices to prove
\[
\frac{3(9-2q)}{5}+\frac{(56+2q)^2}{560-80q+2q^2+44r}\geq 11.
\]
Since
\[
3(x+y+z)xyz\leq (xy+yz+zx)^2,
\]we have
\[
r\leq \frac{q^2}{3},
\]and consequently,
\[
\frac{(56+2q)^2}{560-80q+2q^2+44r}\geq \frac{(56+2q)^2}{560-80q+2q^2+44\cdot \frac{q^2}{3}}.
\]Thus, it suffices to prove that
\[
\frac{3(9-2q)}{5}+\frac{(56+2q)^2}{560-80q+2q^2+44\cdot \frac{q^2}{3}}\geq 11.
\]
This simplifies to
\[
(1-3q)q^2\geq 0,
\]which is evidently true. Therefore, the original inequality holds.
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