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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
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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
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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
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A cyclic inequality
JK1603JK   0
13 minutes ago
Source: unknown
Let a,b,c be real numbers. Prove that a^6+b^6+c^6\ge 2(a+b+c)(ab+bc+ca)(a-b)(b-c)(c-a).
0 replies
JK1603JK
13 minutes ago
0 replies
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IMO 2024 Prediction
GreenTea2593   100
N 16 minutes ago by ohiorizzler1434
Source: inspired by math90
Hello Aops! Since IMO 2024 is less than a week away,
What are your predictions for the category of each problem at IMO 2024?

If you want to write your prediction, please write it in the form ABC DEF
Where A,B,C,D,E,F are problems 1,2,3,4,5,6 respectively. Each letter should be A,C,G or N.

Rules:
1. Problems 1,2,4,5 are distinct categories.
2. Each day consists of 3 distinct categories.

Edit : the answer is ANC GCA
100 replies
GreenTea2593
Jul 10, 2024
ohiorizzler1434
16 minutes ago
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Cyclic ine
m4thbl3nd3r   1
N 17 minutes ago by JK1603JK
Let $a,b,c>0$ such that $a+b+c=3$. Prove that $$a^3b+b^3c+c^3a+9abc\le 12$$
1 reply
m4thbl3nd3r
Yesterday at 3:17 PM
JK1603JK
17 minutes ago
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Mysterious 42
steven_zhang123   0
28 minutes ago
Source: China TST 2001 Quiz 5 P3
Consider the problem of expressing $42$ as \(42 = x^3 + y^3 + z^3 - w^2\), where \(x, y, z, w\) are integers. Determine the number of ways to represent $42$ in this form and prove your conclusion.
0 replies
steven_zhang123
28 minutes ago
0 replies
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Maximizing
steven_zhang123   0
an hour ago
Source: China TST 2001 Quiz 5 P2
Find the largest positive real number \( c \) such that for any positive integer \( n \), satisfies \(\{ \sqrt{7n} \} \geq \frac{c}{\sqrt{7n}}\).
0 replies
steven_zhang123
an hour ago
0 replies
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Quality FE
pablock   36
N an hour ago by ehuseyinyigit
Source: 2020 Iberoamerican #5
Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that $$f(xf(x-y))+yf(x)=x+y+f(x^2),$$for all real numbers $x$ and $y.$
36 replies
pablock
Nov 17, 2020
ehuseyinyigit
an hour ago
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Problem 4 (second day)
darij grinberg   91
N an hour ago by Marcus_Zhang
Source: IMO 2004 Athens
Let $n \geq 3$ be an integer. Let $t_1$, $t_2$, ..., $t_n$ be positive real numbers such that \[n^2 + 1 > \left( t_1 + t_2 + \cdots + t_n \right) \left( \frac{1}{t_1} + \frac{1}{t_2} + \cdots + \frac{1}{t_n} \right).\] Show that $t_i$, $t_j$, $t_k$ are side lengths of a triangle for all $i$, $j$, $k$ with $1 \leq i < j < k \leq n$.
91 replies
darij grinberg
Jul 13, 2004
Marcus_Zhang
an hour ago
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Whiteboard magic again
navi_09220114   2
N an hour ago by mashumaro
Source: Malaysian IMO TST 2025 P5
Fix positive integers $n$ and $k$, and $2n$ positive (not neccesarily distinct) real numbers $a_1,\cdots, a_n$, $b_1, \cdots, b_n$. An equation is written on a whiteboard: $$t=*\times*\times\cdots\times*$$where $t$ is a fixed positive real number, with exactly $k$ asterisks.

Ebi fills each asterisk with a number from $a_1, a_2,\cdots, a_n$, while Rubi fills each asterisk with a number from $b_1, b_2,\cdots, b_n$, so that the equation on the whiteboard is correct. Suppose for every positive real number $t$, the number of ways for Ebi and Rubi to do so are equal.

Prove that the sequences $a_1,\cdots, a_n$ and $b_1, \cdots, b_n$ are permutations of each other.

(Note: $t=a_1a_2a_3$ and $t=a_2a_3a_1$ are considered different ways to fill the asterisks, and the chosen terms need not be distinct, for example $t=a_1a_1a_2$.)

Proposed by Wong Jer Ren
2 replies
navi_09220114
Yesterday at 1:01 PM
mashumaro
an hour ago
J
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Math Olympiad Workshops
kokcio   0
2 hours ago
Hello Math Enthusiasts!

I'm excited to announce a series of free Math Olympiad Workshops designed to help you sharpen your problem-solving skills in preparation for competitions. Whether you're a beginner or a seasoned competitor, these workshops aim to provide a supportive, challenging, and collaborative environment to explore advanced math topics.

Workshop Overview

Duration: 6 months (with the possibility of extending based on participant interest)

Structure: Weekly cycles, each dedicated to one of the main areas of Math Olympiad:
Week 1: Number Theory
Week 2: Geometry
Week 3: Algebra
Week 4: Combinatorics

Weekly Format
Monday: Problem Set Release: Approximately 30 problems will be posted covering the week's topic, which you will have chance to discuss.
Throughout the Week:
Theory Notes: I will share helpful theory and insights relevant to the problem set, giving you the tools you need to approach the problems.
Submission Opportunity: You can work on the problems and submit your solutions. I’ll review your work and provide feedback.
End of the Week: Solutions Post: I’ll release detailed solutions to all problems from the problem set.
Leaderboard: For those interested, we can maintain a table tracking participants who solve the most problems during the week.

Cycle Finale – Mock Contest
At the end of each 4-week cycle, we’ll host a Mock Contest featuring 4 problems (one from each topic). This is a great chance to simulate the competition environment and test your skills in a timed setting. I will review and provide feedback on your contest submissions.

Starting date: June 2

How to participate? Just write /signup under this post.

I believe these workshops will provide a comprehensive, engaging, and collaborative way to tackle Math Olympiad problems. I'm looking forward to seeing your creativity and problem-solving prowess!
If you have any questions or suggestions, please leave a comment below.
0 replies
kokcio
2 hours ago
0 replies
J
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three "old" circles and four concurrent lines
pohoatza   50
N 2 hours ago by Sanjana42
Source: IMO Shortlist 2006, Geometry 6, AIMO 2007, TST 3, P3
Circles $ w_{1}$ and $ w_{2}$ with centres $ O_{1}$ and $ O_{2}$ are externally tangent at point $ D$ and internally tangent to a circle $ w$ at points $ E$ and $ F$ respectively. Line $ t$ is the common tangent of $ w_{1}$ and $ w_{2}$ at $ D$. Let $ AB$ be the diameter of $ w$ perpendicular to $ t$, so that $ A, E, O_{1}$ are on the same side of $ t$. Prove that lines $ AO_{1}$, $ BO_{2}$, $ EF$ and $ t$ are concurrent.
50 replies
pohoatza
Jun 28, 2007
Sanjana42
2 hours ago
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FE on Stems
mathscrazy   6
N 3 hours ago by SatisfiedMagma
Source: STEMS 2025 Category B4, C3
Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for all $x,y\in \mathbb{R}$, \[xf(y+x)+(y+x)f(y)=f(x^2+y^2)+2f(xy)\]Proposed by Aritra Mondal
6 replies
mathscrazy
Dec 29, 2024
SatisfiedMagma
3 hours ago
J
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number theory question?
jag11   2
N 3 hours ago by jag11
Find the smallest positive integer n such that n is a multiple of 11, n +1 is a multiple of 10, n + 2 is a
multiple of 9, n + 3 is a multiple of 8, n +4 is a multiple of 7, n +5 is a multiple of 6, n +6 is a multiple of
5, n + 7 is a multiple of 4, n + 8 is a multiple of 3, and n + 9 is a multiple of 2.

I tried doing the mods and simplifying it but I'm kinda confused.
2 replies
jag11
3 hours ago
jag11
3 hours ago
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Complex numbers should be easy
RenheMiResembleRice   2
N 4 hours ago by RandomMathGuy500
Source: Wenjing Kong
I cant do the last part. :(
2 replies
RenheMiResembleRice
Friday at 8:32 AM
RandomMathGuy500
4 hours ago
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Mathhhhh
mathbetter   13
N 4 hours ago by ayeshabatool
Three turtles are crawling along a straight road heading in the same
direction. "Two other turtles are behind me," says the first turtle. "One turtle is
behind me and one other is ahead," says the second. "Two turtles are ahead of me
and one other is behind," says the third turtle. How can this be possible?
13 replies
mathbetter
Mar 20, 2025
ayeshabatool
4 hours ago
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Graph Theory
JetFire008   1
N Friday at 4:26 PM by JetFire008
Prove that for any Hamiltonian cycle, if it contain edge $e$, then it must not contain edge $e'$.
1 reply
JetFire008
Friday at 4:22 PM
JetFire008
Friday at 4:26 PM
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Graph Theory
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Reveal topic tags
graph theory
hamiltonian graph
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JetFire008
105 posts
JetFire008
#1 h  Friday at 4:22 PM
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Prove that for any Hamiltonian cycle, if it contain edge $e$, then it must not contain edge $e'$.
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JetFire008
105 posts
JetFire008
#2 h  Friday at 4:26 PM
Y by
Let $S=\{x_1, x_2, ..., x_n\}$ where $n \ge 3$ be the set of vertices on the plane. The distance between two arbitrary vertices is no less than $1$. Prove that there are at most $3n-6$ pairs of vertices whose distances are $1$.
This post has been edited 1 time. Last edited by JetFire008, Friday at 4:26 PM
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