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a My Retirement & New Leadership at AoPS
rrusczyk   1609
N a few seconds ago by ailiuda30
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
1609 replies
+9 w
rrusczyk
Mar 24, 2025
ailiuda30
a few seconds 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:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
1 viewing
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
J
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The sheep problem
ysn613   12
N 8 minutes ago by xHypotenuse
a) If I have three sheep, how can I arrange them so that they are all an equal distance away from each other?
b)If I have four sheep, how can I do the same thing as I wanted to do in part a)?
12 replies
ysn613
Today at 3:49 PM
xHypotenuse
8 minutes ago
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The daily problem!
Leeoz   31
N 16 minutes ago by Marcus_Antonio
Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)

Please hide solutions and answers, hints are fine though! :)

The first problem is:
[quote=March 21st Problem]Alice flips a fair coin until she gets 2 heads in a row, or a tail and then a head. What is the probability that she stopped after 2 heads in a row? Express your answer as a common fraction.[/quote]
31 replies
Leeoz
Mar 21, 2025
Marcus_Antonio
16 minutes ago
J
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Newton Sums
mithu542   6
N 26 minutes ago by Soupboy0
Should I memorize Newton's Sums? I already know the first two, but do you think it is worthy to memorize some more (especially 3)?

Website about Newton Sums
6 replies
mithu542
Today at 1:59 AM
Soupboy0
26 minutes ago
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If you'll be at the National MathCounts competition
Chatelet1   10
N 27 minutes ago by Soupboy0
Don't forget to greet Richard if encountered in the hallway. He's retiring early at 53, so it's a good chance to wish him well!

Seminar on May 11:
Preparing Strong Math Students for College and Careers
9:30 – 10:30am ET | Anacostia Ballroom
Presented by Richard Rusczyk, Art of Problem Solving Founder.

Retirement announcement from Richard (3/24/2025)

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 deeply grateful to all the AoPS team members who have helped build AoPS. I’m also thankful for the many supporters who provided inspiration and encouragement along the way.

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.
10 replies
Chatelet1
Mar 24, 2025
Soupboy0
27 minutes ago
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Cauchy-Schwarz 2
prtoi   2
N 2 hours ago by mpcnotnpc
Source: Handout by Samin Riasat
if $a^2+b^2+c^2+d^2=4$, prove that:
$\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a}\ge4$
2 replies
prtoi
6 hours ago
mpcnotnpc
2 hours ago
J
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Maximum of Incenter-triangle
mpcnotnpc   2
N 3 hours ago by mpcnotnpc
Triangle $\Delta ABC$ has side lengths $a$, $b$, and $c$. Select a point $P$ inside $\Delta ABC$, and construct the incenters of $\Delta PAB$, $\Delta PBC$, and $\Delta PAC$ and denote them as $I_A$, $I_B$, $I_C$. What is the maximum area of the triangle $\Delta I_A I_B I_C$?
2 replies
mpcnotnpc
Yesterday at 6:24 PM
mpcnotnpc
3 hours ago
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Induction
Mathlover_1   1
N 3 hours ago by Primeniyazidayi
Hello, can you share links of same interesting induction problems in algebra
1 reply
Mathlover_1
Mar 24, 2025
Primeniyazidayi
3 hours ago
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equal angles
jhz   3
N 3 hours ago by DottedCaculator
Source: 2025 CTST P16
In convex quadrilateral $ABCD, AB \perp AD, AD = DC$. Let $ E$ be a point on side $BC$, and $F$ be a point on the extension of $DE$ such that $\angle ABF = \angle DEC>90^{\circ}$. Let $O$ be the circumcenter of $\triangle CDE$, and $P$ be a point on the side extension of $FO$ satisfying $FB =FP$. Line BP intersects AC at point Q. Prove that $\angle AQB =\angle DPF.$
3 replies
jhz
Today at 12:56 AM
DottedCaculator
3 hours ago
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Nordic 2025 P2
anirbanbz   7
N 3 hours ago by Mathdreams
Source: Nordic 2025
Let $p$ be a prime and suppose $2^{2p} \equiv 1 (\text{mod}$ $ 2p+1)$ is prime. Prove that $2p+1$ is prime$^{1}$

$^{1}$This is a special case of Pocklington's theorem. A proof of this special case is required.
7 replies
anirbanbz
Yesterday at 12:35 PM
Mathdreams
3 hours ago
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Lines AD, BE, and CF are concurrent
orl   45
N 4 hours ago by Mapism
Source: IMO Shortlist 2000, G3
Let $O$ be the circumcenter and $H$ the orthocenter of an acute triangle $ABC$. Show that there exist points $D$, $E$, and $F$ on sides $BC$, $CA$, and $AB$ respectively such that \[ OD + DH = OE + EH = OF + FH\] and the lines $AD$, $BE$, and $CF$ are concurrent.
45 replies
orl
Aug 10, 2008
Mapism
4 hours ago
J
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Find f such that $f(f(f(x)))=x : \forall x \in R $
Lang_Tu_Mua_Bui   3
N 4 hours ago by jasperE3
Find f such that $f(f(f(x)))=x : \forall x \in R $
3 replies
Lang_Tu_Mua_Bui
Dec 2, 2015
jasperE3
4 hours ago
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AM-GM problem from a handout
prtoi   1
N 4 hours ago by Primeniyazidayi
Prove that:
$\frac{a}{b}+\frac{b}{c}+\frac{c}{a}+\frac{3(abc)^{1/3}}{a+b+c}\ge3+n$
1 reply
prtoi
Today at 4:09 PM
Primeniyazidayi
4 hours ago
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Cauchy Schwarz 4
prtoi   1
N 4 hours ago by Primeniyazidayi
Source: Zhautykov Olympiad 2008
Let a, b, c be positive real numbers such that abc = 1.
Show that
$\frac{1}{b(a+b)}+\frac{1}{b(a+b)}+\frac{1}{b(a+b)}\ge\frac{3}{2}$
1 reply
prtoi
6 hours ago
Primeniyazidayi
4 hours ago
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Cauchy-Schwarz 1
prtoi   2
N 4 hours ago by Primeniyazidayi
Source: Handout by Samin Riasat
$\frac{a}{b+c}+\frac{b}{c+d}+\frac{c}{d+a}+\frac{d}{a+b}\ge2$
2 replies
prtoi
6 hours ago
Primeniyazidayi
4 hours ago
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please help how to solve systematically?
NC123   1
N Mar 24, 2025 by ostriches88
I am able to get the answer, but curious how you would solve it?
1 reply
NC123
Mar 24, 2025
ostriches88
Mar 24, 2025
J
please help how to solve systematically?
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NC123
3 posts
NC123
#1 h  Mar 24, 2025, 7:15 AM
Y by
I am able to get the answer, but curious how you would solve it?
Attachments:
This post has been edited 2 times. Last edited by NC123, Mar 24, 2025, 4:06 PM
Reason: better wording
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ostriches88
1527 posts
ostriches88
#2 h  Mar 24, 2025, 12:09 PM
Y by
not great
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