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a My Retirement & New Leadership at AoPS
rrusczyk   1345
N 44 minutes ago by GoodGamer123
I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE
1345 replies
rrusczyk
Monday at 6:37 PM
GoodGamer123
44 minutes ago
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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:
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0 replies
jlacosta
Mar 2, 2025
0 replies
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7 triangles in a square
gghx   2
N 13 minutes ago by lightsynth123
Source: SMO junior 2024 Q3
Seven triangles of area $7$ lie in a square of area $27$. Prove that among the $7$ triangles there are $2$ that intersect in a region of area not less than $1$.
2 replies
gghx
Oct 12, 2024
lightsynth123
13 minutes ago
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Probability-hard
Noname23   0
23 minutes ago
problem
0 replies
Noname23
23 minutes ago
0 replies
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Find the value
sqing   0
28 minutes ago
Source: Hunan changsha 2025
Let $ a,b,c $ be real numbers such that $ abc\neq 0,2a-b+c= 0 $ and $ a-2b-c=0. $ Find the value of $\frac{a^2+b^2+c^2}{ab+bc+ca}.$
Let $ a,b,c $ be real numbers such that $ abc\neq 0,a+2b+3c= 0 $ and $ 2a+3b+4c=0. $ Find the value of $\frac{ab+bc+ca}{a^2+b^2+c^2}.$
0 replies
sqing
28 minutes ago
0 replies
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n-variable inequality
ABCDE   65
N an hour ago by LMat
Source: 2015 IMO Shortlist A1, Original 2015 IMO #5
Suppose that a sequence $a_1,a_2,\ldots$ of positive real numbers satisfies \[a_{k+1}\geq\frac{ka_k}{a_k^2+(k-1)}\]for every positive integer $k$. Prove that $a_1+a_2+\ldots+a_n\geq n$ for every $n\geq2$.
65 replies
ABCDE
Jul 7, 2016
LMat
an hour ago
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digit reversing and divisibility
roundtablepizza   6
N Yesterday at 11:47 PM by roundtablepizza
an interesting problem i thought of:

for what integers k will the following statement be true: if k divides a number, then it will also divide that number reversed.

for example, since 3 divides 321, it also divides 123.

i know this applies for 3, 9, and 11(maybe??) but are there infinitely many more values of k?
6 replies
roundtablepizza
Mar 24, 2025
roundtablepizza
Yesterday at 11:47 PM
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ARML math competetion
purpledonutdragon   3
N Yesterday at 9:43 PM by AbhayAttarde01
Do you guys have any tips for ARML? What are some concepts that will be very helpful in ARML?
3 replies
purpledonutdragon
Yesterday at 12:39 PM
AbhayAttarde01
Yesterday at 9:43 PM
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function???
Math2030   1
N Yesterday at 8:49 PM by SomeonecoolLovesMaths
find all functions f: \mathbb{R} \to \mathbb{R} satisfy:
3f(\dfrac{x-1}{3x+2})-5f(\dfrac{1-x}{x-2})=\dfrac{8}{x-1}, \quad \forall x\notin \{0, \dfrac{-2}{3},1,2\}


1 reply
Math2030
Yesterday at 3:22 PM
SomeonecoolLovesMaths
Yesterday at 8:49 PM
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functions false or true
Math2030   2
N Yesterday at 8:48 PM by SomeonecoolLovesMaths
find all functions f: \mathbb{R} \to \mathbb{R} that satisfy the functional equation:


f(x^2 f(x) + f(y)) = (f(x))^3 + f(y), \quad \forall x, y \in \mathbb{R}
2 replies
Math2030
Yesterday at 3:05 PM
SomeonecoolLovesMaths
Yesterday at 8:48 PM
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3D Geometry Problem
ReticulatedPython   0
Yesterday at 8:12 PM
Three mutually tangent non-degenerate spheres rest on a plane. Let their centers be $A, B$, and $C$. The spheres with centers $A, B$, and $C$ touch the plane at $P, Q$, and $R$, respectively. Prove that $$\frac{1}{AP}+\frac{1}{BQ}+\frac{1}{CR}+PQ+RQ+PR \ge 6\sqrt{2}$$
0 replies
ReticulatedPython
Yesterday at 8:12 PM
0 replies
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Ask mininum
TangenT-maTh-   3
N Yesterday at 4:10 PM by rchokler
Find the mininum value of function$f(x)=\cos^2 x-4\cos x-2\sqrt{3}\sin x$
3 replies
TangenT-maTh-
Mar 13, 2025
rchokler
Yesterday at 4:10 PM
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Problem of set
toanrathay   0
Yesterday at 3:36 PM
A set \( A \subset \mathbb{R} \) is called a $\textit{nice}$ if it satisfies the following conditions:
$i)$ \( A \) contains at least two elements.
$ii)$ For all \( x, y \in A \) with \( x \neq y \), we have \( xy(x+y) \neq 0 \), and among the two numbers \( x+y \) and \( xy \), exactly one is rational.
$iii)$ For all \( x \in A \), \( x^2 \) is irrational.
What is the maximum number of elements that \( A \) can have?


0 replies
toanrathay
Yesterday at 3:36 PM
0 replies
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combinations, probability
Chanome   5
N Yesterday at 3:09 PM by ReticulatedPython
Given a fair \( n \)-sided die with sides \( 1, 2, \dots, n \), consider the following game:

1. Roll the die. If the roll results in \( n \), you win immediately.
2. Otherwise, roll again. However, if the second roll is not greater than the previous roll, you lose.
3. Continue rolling until either:
- You roll \( n \), in which case you win.
- Or, your current roll is not greater than your previous roll, in which case you lose.

For example, when \( n = 4 \):
- Rolls \( 1, 3, 4 \): Win
- Rolls \( 3, 1 \): Lose
- Rolls \( 1, 2, 2 \): Lose
- Rolls \( 2, 4 \): Win

Find a formula to find the probability of winning for any given \( n \).
5 replies
Chanome
Monday at 2:36 PM
ReticulatedPython
Yesterday at 3:09 PM
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Inequalities
sqing   31
N Yesterday at 12:55 PM by sqing
Let $ a,b>0 $ and $ \frac{1}{a}+\frac{1}{b}=1. $ Prove that
$$(a^2-a+1)(b^2-b+1) \geq 9$$$$ (a^2-a+b+1)(b^2-b+a+1) \geq 25$$Let $ a,b>0 $ and $ \frac{1}{a}+\frac{1}{b}=\frac{2}{3}. $ Prove that
$$(a+8)(a^2-a+b+2)(b^2-b+5)\geq1331$$$$(a+10)(a^2-a+b+4)(b^2-b+7)\geq2197$$
31 replies
sqing
Mar 10, 2025
sqing
Yesterday at 12:55 PM
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Inequality
MathsII-enjoy   1
N Yesterday at 12:13 PM by sqing
A good inequality problem :coolspeak:
1 reply
MathsII-enjoy
Yesterday at 11:00 AM
sqing
Yesterday at 12:13 PM
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Obsolete NT
GreekIdiot   1
N Mar 23, 2025 by amapstob
Source: older isl
Find all $n \in \mathbb{N}$ greater than $1$, such that, if $gcd(a,b)=1$, then $a \equiv b \: mod \: n \iff ab \equiv 1 \: mod \: n$
1 reply
GreekIdiot
Mar 23, 2025
amapstob
Mar 23, 2025
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Obsolete NT
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Reveal topic tags
number theory
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Source: older isl
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GreekIdiot
124 posts
GreekIdiot
#1 h  Mar 23, 2025, 1:29 PM
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Find all $n \in \mathbb{N}$ greater than $1$, such that, if $gcd(a,b)=1$, then $a \equiv b \: mod \: n \iff ab \equiv 1 \: mod \: n$
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amapstob
19 posts
amapstob
#2 h  Mar 23, 2025, 3:08 PM
Y by
https://artofproblemsolving.com/community/c6h15033p106668
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