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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 Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
Eventually constant sequence with condition
PerfectPlayer   0
44 minutes ago
Source: Turkey TST 2025 Day 3 P8
A positive real number sequence $a_1, a_2, a_3,\dots $ and a positive integer \(s\) is given.
Let $f_n(0) = \frac{a_n+\dots+a_1}{n}$ and for each $0<k<n$
\[f_n(k)=\frac{a_n+\dots+a_{k+1}}{n-k}-\frac{a_k+\dots+a_1}{k}\]Then for every integer $n\geq s,$ the condition
\[a_{n+1}=\max_{0\leq k<n}(f_n(k))\]is satisfied. Prove that this sequence must be eventually constant.
0 replies
PerfectPlayer
44 minutes ago
0 replies
Number of modular sequences with different residues
PerfectPlayer   0
an hour ago
Source: Turkey TST 2025 Day 3 P9
Let \(n\) be a positive integer. For every positive integer $1 \leq k \leq n$ the sequence ${\displaystyle {\{ a_{i}+ki\}}_{i=1}^{n }}$ is defined, where $a_1,a_2, \dots ,a_n$ are integers. Among these \(n\) sequences, for at most how many of them does all the elements of the sequence give different remainders when divided by \(n\)?
0 replies
PerfectPlayer
an hour ago
0 replies
Find max no. of gangsters
sk2005   4
N an hour ago by flower417477
In Chicago, there are 36 criminal gangs, some of which are at war with
each other. Each gangster belongs to several gangs and every pair of gangsters
belongs to a different set of gangs. It is known that no gangster is a member of
two gangs which are at war with each other. Furthermore, each gang that some
gangster does not belong to is at war with some gang he does belong to. What is
the largest possible number of gangsters in Chicago?
4 replies
sk2005
Sep 13, 2021
flower417477
an hour ago
super duper ez radax problem
iStud   1
N an hour ago by MathLuis
Source: Monthly Contest KTOM March 2025 P1 Essay
Given an acute triangle $ABC$ with $BC<AB<AC$. Points $D$ and $E$ are on $AB$ and $AC$ respectively such that $DB=BC=CE$. Lines $CD$ and $BE$ meet at $F$. $I$ is the incenter of $\triangle{ABC}$ and $H$ is the orthocenter of $\triangle{DEF}$. $\omega_b$ and $\omega_c$ are circles with diameter $BD$ and $CE$, respectively, intersecting each other at points $X$ and $Y$. Prove that $I$ and $H$ lie on $XY$.

Hint
1 reply
iStud
an hour ago
MathLuis
an hour ago
[Registration Open] Mustang Math Tournament 2025
MustangMathTournament   31
N an hour ago by ethan2011
Mustang Math is excited to announce that registration for our annual tournament, MMT 2025, is open! This year, we are bringing our tournament to 9 in-person locations, as well as online!

Locations include: Colorado, Norcal, Socal, Georgia, Illinois, Massachusetts, New Jersey, Nevada, Washington, and online. For registration and more information, check out https://mustangmath.com/competitions/mmt-2025.

MMT 2025 is a math tournament run by a group of 150+ mathematically experienced high school and college students who are dedicated to providing a high-quality and enjoyable contest for middle school students. Our tournament centers around teamwork and collaboration, incentivizing students to work with their teams not only to navigate the challenging and interesting problems of the tournament but also to develop strategies to master the unique rounds. This includes a logic puzzle round, a strategy-filled hexes round, a race-like gallop round, and our trademark ‘Mystery Mare’ round!

Awards:
[list]
[*] Medals for the top teams
[*] Shirts, pins, stickers and certificates for all participants
[*] Additional awards provided by our wonderful sponsors!
[/list]

We are also holding a free MMT prep seminar from 3/15-3/16 to help students prepare for the upcoming tournament. Join the Google Classroom! https://classroom.google.com/c/NzQ5NDUyNDY2NjM1?cjc=7sogth4
31 replies
MustangMathTournament
Mar 8, 2025
ethan2011
an hour ago
how do we find a construction?
iStud   0
an hour ago
Source: Monthly Contest KTOM March 2025 P4 Essay
Given a chess board $n\times n$ with $n>3$ with all the unit squares are initially white coloured. Every move, we can turn the color (from white to black or otherwise) from the 5 unit squares that form this T-pentomino which can be rotated or reflexed (see the image below). Determine all natural numbers $n$ such that all unit squares on the board can be made into all black after a finite number of moves.
0 replies
iStud
an hour ago
0 replies
unnecessary wrapped FE on Q
iStud   0
an hour ago
Source: Monthly Contest KTOM March 2025 P3 Essay
Find all functions $f:\mathbb{Q}\to\mathbb{Q}$ such that
\[f(f(f(\frac{x+y}{2}))+x+y)=f(x)+f(y)+f(\frac{x+y}{2})\]for all rational numbers $x,y$.

Hint
0 replies
iStud
an hour ago
0 replies
Inspired by Mihaela Berindeanu
sqing   2
N an hour ago by sqing
Source: Own
Let $ a,b,c>0  . $ Prove that
$$(4a+b+c)(a+b)(b+c)(c+a)\geq (ab+bc+ca)(2a+b+c)^2$$
2 replies
sqing
Yesterday at 2:08 PM
sqing
an hour ago
The Sums of Elements in Subsets
bobaboby1   1
N an hour ago by bobaboby1
Given a finite set \( X = \{x_1, x_2, \ldots, x_n\} \), and the pairwise comparison of the sums of elements of all its subsets (with the empty set defined as having a sum of 0), which amounts to \( \binom{2}{2^n} \) inequalities, these given comparisons satisfy the following three constraints:

1. The sum of elements of any non-empty subset is greater than 0.
2. For any two subsets, removing or adding the same elements does not change their comparison of the sums of elements.
3. For any two disjoint subsets \( A \) and \( B \), if the sums of elements of \( A \) and \( B \) are greater than those of subsets \( C \) and \( D \) respectively, then the sum of elements of the union \( A \cup B \) is greater than that of \( C \cup D \).

The question is: Does there necessarily exist a positive solution \( (x_1, x_2, \ldots, x_n) \) that satisfies all these conditions?
1 reply
bobaboby1
Mar 12, 2025
bobaboby1
an hour ago
average FE
KevinYang2.71   76
N 2 hours ago by Maximilian113
Source: USAJMO 2024/5
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ that satisfy
\[
f(x^2-y)+2yf(x)=f(f(x))+f(y)
\]for all $x,y\in\mathbb{R}$.

Proposed by Carl Schildkraut
76 replies
KevinYang2.71
Mar 21, 2024
Maximilian113
2 hours ago
Max amount of equal numbers among (a_i^2 + a_j^2)/(a_i + a_j)
mshtand1   1
N 2 hours ago by Rushery_10
Source: Ukrainian Mathematical Olympiad 2025. Day 2, Problem 9.8
Given $2025$ pairwise distinct positive integer numbers \(a_1, a_2, \ldots, a_{2025}\), find the maximum possible number of equal numbers among the fractions of the form
\[
\frac{a_i^2 + a_j^2}{a_i + a_j}
\]
Proposed by Mykhailo Shtandenko
1 reply
mshtand1
Mar 14, 2025
Rushery_10
2 hours ago
Combinatorics from Iranian TST 2017
bgn   20
N 2 hours ago by ezpotd
Source: Iranian TST 2017, first exam, day1, problem 2
In the country of Sugarland, there are $13$ students in the IMO team selection camp.
$6$ team selection tests were taken and the results have came out. Assume that no students have the same score on the same test.To select the IMO team, the national committee of math Olympiad have decided to choose a permutation of these $6$ tests and starting from the first test, the person with the highest score between the remaining students will become a member of the team.The committee is having a session to choose the permutation.
Is it possible that all $13$ students have a chance of being a team member?

Proposed by Morteza Saghafian
20 replies
bgn
Apr 5, 2017
ezpotd
2 hours ago
JSMCR Results
FuturePanda   14
N 3 hours ago by Pengu14
Hi everyone,

Did anyone get their JSMCR decisions back yet? They were supposed to release on 2/28

Thanks!
14 replies
FuturePanda
Mar 1, 2025
Pengu14
3 hours ago
AMC 10.........
BAM10   8
N 3 hours ago by ChickensEatGrass
I'm in 8th grade and have never taken the AMC 10. I am currently in alg2. I have scored 20 on AMC 8 this year and 34 on the chapter math counts last year. Can I qualify for AIME. Also what should I practice AMC 10 next year?
8 replies
BAM10
Mar 2, 2025
ChickensEatGrass
3 hours ago
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   10
N Yesterday at 3:02 PM by RainbowSquirrel53B
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary


Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


10 replies
audio-on
Jan 26, 2025
RainbowSquirrel53B
Yesterday at 3:02 PM
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
G H J
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audio-on
507 posts
#1 • 7 Y
Y by stuffedmath, christinaa.luu, manaleec, KevinYang2.71, EveningDawn, KnowingAnt, crazyeyemoody907
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary


Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!
Z K Y
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Ruegerbyrd
1033 posts
#6 • 1 Y
Y by ChampionGirl
why only middle school :(
Z K Y
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christinaa.luu
2 posts
#7
Y by
Will the online award ceremony be recorded if I can’t attend live?
Z K Y
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audio-on
507 posts
#8
Y by
christinaa.luu wrote:
Will the online award ceremony be recorded if I can’t attend live?

Yes, we will record the online award ceremony :)
You can access recordings from previous years on our YouTube channel or on our website under the result from each year (for example, the slide presentation and recording link for 2024 are under "Additional Links")
Z K Y
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SanrioSmarties05
149 posts
#9
Y by
How exactly will this work?
Z K Y
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mirzakhani12
3 posts
#10
Y by
This sounds like a great initiative! What steps can students take to prepare?
Z K Y
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audio-on
507 posts
#12
Y by
SanrioSmarties05 wrote:
How exactly will this work?

After applications open on 3/22, you'll have about a month to complete the application!
We will post a Submittable link closer to the competition on our website, and you can find the problem set + essay questions there.
Applications will be filled out on Submittable.
Z K Y
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audio-on
507 posts
#13
Y by
mirzakhani12 wrote:
This sounds like a great initiative! What steps can students take to prepare?

Students will be tested on a variety of topics. The problem set is mainly math, although having a bit of computer science knowledge could help.
I would recommend looking at the past competitions under our past contests tab here where you can find the problem set + solutions for 2021 - 2023. You can find the problems and solutions from last year's competition here.

Hope this helps!
This post has been edited 1 time. Last edited by audio-on, Feb 10, 2025, 7:33 PM
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christinaa.luu
2 posts
#14
Y by
Do I need a lot of experience in AI and programming to be able to participate?
Z K Y
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angie.
314 posts
#15
Y by
christinaa.luu wrote:
Do I need a lot of experience in AI and programming to be able to participate?

No, you don't need any experience in AI or programming to participate! Most of the contest is logic based, and the CS involves simple pseudocode designed to be accessible for everyone.
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RainbowSquirrel53B
583 posts
#16
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How many contestants are there usually?
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