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a My Retirement & New Leadership at AoPS
rrusczyk   1408
N 7 minutes ago by FrenchFry99
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
1408 replies
rrusczyk
Monday at 6:37 PM
FrenchFry99
7 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:
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
J
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The three lines AA', BB' and CC' meet on the line IO
WakeUp   44
N 26 minutes ago by ihategeo_1969
Source: Romanian Master Of Mathematics 2012
Let $ABC$ be a triangle and let $I$ and $O$ denote its incentre and circumcentre respectively. Let $\omega_A$ be the circle through $B$ and $C$ which is tangent to the incircle of the triangle $ABC$; the circles $\omega_B$ and $\omega_C$ are defined similarly. The circles $\omega_B$ and $\omega_C$ meet at a point $A'$ distinct from $A$; the points $B'$ and $C'$ are defined similarly. Prove that the lines $AA',BB'$ and $CC'$ are concurrent at a point on the line $IO$.

(Russia) Fedor Ivlev
44 replies
+1 w
WakeUp
Mar 3, 2012
ihategeo_1969
26 minutes ago
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Nice problemm
hanzo.ei   0
31 minutes ago

Consider the sequence $(a_n)$ defined as follows:
\[ a_1 = \frac{\sqrt{6}}{3}, \quad a_{n+1} = a_n + \frac{1}{3a_n}, \quad \forall n \in \mathbb{N}. \]
a, Prove that
\[ 0 \le a_n \sqrt{6} - 2\sqrt{n} \le \frac{1}{4\sqrt{n}} \Bigl( 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n} \Bigr), \quad \forall n \in \mathbb{N}. \]b,For each $n \in \mathbb{N}$, define
\[ b_n = \frac{3a_n^2 - 2n - 1}{\ln(n+1)}. \]Compute the limit $\displaystyle \lim_{n \to \infty} b_n.$
0 replies
hanzo.ei
31 minutes ago
0 replies
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i need help
MR.1   4
N 34 minutes ago by GreekIdiot
Source: help
can you guys tell me problems about fe in $R+$(i know $R$ well). i want to study so if you guys have some easy or normal problems please send me
4 replies
MR.1
Mar 15, 2025
GreekIdiot
34 minutes ago
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IMO 2016 Problem 1
quangminhltv99   147
N an hour ago by bjump
Source: IMO 2016
Triangle $BCF$ has a right angle at $B$. Let $A$ be the point on line $CF$ such that $FA=FB$ and $F$ lies between $A$ and $C$. Point $D$ is chosen so that $DA=DC$ and $AC$ is the bisector of $\angle{DAB}$. Point $E$ is chosen so that $EA=ED$ and $AD$ is the bisector of $\angle{EAC}$. Let $M$ be the midpoint of $CF$. Let $X$ be the point such that $AMXE$ is a parallelogram. Prove that $BD,FX$ and $ME$ are concurrent.
147 replies
quangminhltv99
Jul 11, 2016
bjump
an hour ago
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AoPS wiki loading slowly?
EaZ_Shadow   17
N an hour ago by Craftybutterfly
I don't know why, but why is that when I try loading to AoPS Wiki, it loads really slow? (I'm using an iPad)
17 replies
EaZ_Shadow
Yesterday at 9:18 PM
Craftybutterfly
an hour ago
J
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integral points
jhz   2
N an hour ago by DottedCaculator
Source: 2025 CTST P17
Prove: there exist integer $x_1,x_2,\cdots x_{10},y_1,y_2,\cdots y_{10}$ satisfying the following conditions:
$(1)$ $|x_i|,|y_i|\le 10^{10} $ for all $1\le i \le 10$
$(2)$ Define the set \[S = \left\{ \left( \sum_{i=1}^{10} a_i x_i, \sum_{i=1}^{10} a_i y_i \right) : a_1, a_2, \cdots, a_{10} \in \{0, 1\} \right\},\]then \(|S| = 1024\)，and any rectangular strip of width 1 covers at most two points of S.
2 replies
+3 w
jhz
Today at 1:14 AM
DottedCaculator
an hour ago
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Functional Equation
AnhQuang_67   1
N an hour ago by zoinkers
Find all functions $f: \mathbb{N} \cup \{0\} \to \mathbb{N} \cup \{0\}$ satisfying: $$f(f(m)+f(n))=m+n, \forall m, n \in \mathbb{N} \cup \{0\}$$
1 reply
AnhQuang_67
2 hours ago
zoinkers
an hour ago
J
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Function on positive integers with two inputs
Assassino9931   1
N 2 hours ago by how_to_what_to
Source: Bulgaria Winter Competition 2025 Problem 10.4
The function $f: \mathbb{Z}_{>0} \times \mathbb{Z}_{>0} \to \mathbb{Z}_{>0}$ is such that $f(a,b) + f(b,c) = f(ac, b^2) + 1$ for any positive integers $a,b,c$. Assume there exists a positive integer $n$ such that $f(n, m) \leq f(n, m + 1)$ for all positive integers $m$. Determine all possible values of $f(2025, 2025)$.
1 reply
Assassino9931
Jan 27, 2025
how_to_what_to
2 hours ago
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Prove that there exists a convex 1990-gon
orl   11
N 2 hours ago by lpieleanu
Source: IMO 1990, Day 2, Problem 6, IMO ShortList 1990, Problem 16 (NET 1)
Prove that there exists a convex 1990-gon with the following two properties :

a.) All angles are equal.
b.) The lengths of the 1990 sides are the numbers $ 1^2$, $ 2^2$, $ 3^2$, $ \cdots$, $ 1990^2$ in some order.
11 replies
orl
Nov 11, 2005
lpieleanu
2 hours ago
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SL 2015 G1: Prove that IJ=AH
Problem_Penetrator   133
N 2 hours ago by maths_enthusiast_0001
Source: IMO 2015 Shortlist, G1
Let $ABC$ be an acute triangle with orthocenter $H$. Let $G$ be the point such that the quadrilateral $ABGH$ is a parallelogram. Let $I$ be the point on the line $GH$ such that $AC$ bisects $HI$. Suppose that the line $AC$ intersects the circumcircle of the triangle $GCI$ at $C$ and $J$. Prove that $IJ = AH$.
133 replies
Problem_Penetrator
Jul 7, 2016
maths_enthusiast_0001
2 hours ago
J
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Circles and Chords
steven_zhang123   1
N 2 hours ago by steven_zhang123
(1) Let \( A \) , \( B \) and \( C \) be points on circle \( O \) divided into three equal parts. Construct three equal circles \( O_1 \), \( O_2 \), and \( O_3 \) tangent to \( O \) internally at points \( A \), \( B \), and \( C \) respectively. Let \( P \) be any point on arc \( AC \), and draw tangents \( PD \), \( PE \), and \( PF \) to circles \( O_1 \), \( O_2 \), and \( O_3 \) respectively. Prove that \( PE = PD + PF \).

(2) Let \( A_1 \), \( A_2 \), \( \cdots \), \( A_n \) be points on circle \( O \) divided into \( n \) equal parts. Construct \( n \) equal circles \( O_1 \), \( O_2 \), \( \cdots \), \( O_n \) tangent to \( O \) internally at \( A_1 \), \( A_2 \), \( \cdots \), \( A_n \). Let \( P \) be any point on circle \( O \), and draw tangents \( PB_1 \), \( PB_2 \), \( \cdots \), \( PB_n \) to circles \( O_1 \), \( O_2 \), \( \cdots \), \( O_n \). If the sum of \( k \) of \( PB_1 \), \( PB_2 \), \( \cdots \), \( PB_n \) equals the sum of the remaining \( n-k \) (where \( n \geq k \geq 1 \)), find all such \( n \).
1 reply
steven_zhang123
Mar 23, 2025
steven_zhang123
2 hours ago
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How is this possible
Craftybutterfly   6
N 4 hours ago by dragonborn56
This is very wrong
6 replies
1 viewing
Craftybutterfly
Today at 4:32 AM
dragonborn56
4 hours ago
J
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k Staff, Please confirm or deny this conjecture
Mango8000   2
N Yesterday at 4:37 PM by jlacosta
It’s seems that there are suspicions about AoPS selling Beast Academy to another company. Is that true? Becuase AoPS online and Beast Academy are connected and it will affect us. I hope that AoPS decides to keep it, but if not, there really isn’t anything we can do.
2 replies
Mango8000
Monday at 9:13 PM
jlacosta
Yesterday at 4:37 PM
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k spotted in blogroll
Major_Monogram   8
N Yesterday at 1:06 PM by Embershed97
I saw this on the AoPS Blogroll. closing it, the page worked normally.
8 replies
Major_Monogram
Mar 22, 2025
Embershed97
Yesterday at 1:06 PM
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J
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delete tag
o.k.oo   5
N Mar 19, 2025 by Zestra
The tag section for the question I shared is deleted after a while. What should not be done? Thanks.
5 replies
o.k.oo
Mar 18, 2025
Zestra
Mar 19, 2025
J
delete tag
G H J
Reveal topic tags
L
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
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o.k.oo
4 posts
o.k.oo
#1 h  Mar 18, 2025, 6:00 PM
Y by
The tag section for the question I shared is deleted after a while. What should not be done? Thanks.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
MathDolphin95
2107 posts
MathDolphin95
#2 h  Mar 18, 2025, 10:48 PM
Y by
o.k.oo wrote:
The tag section for the question I shared is deleted after a while. What should not be done? Thanks.

not quite sure what you mean... do you have a screenshot?
Z K Y
The post below has been deleted. Click to close.
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jkim0656
339 posts
jkim0656
#3 h  Mar 18, 2025, 11:03 PM
Y by
...just make a new tag?...
Z K Y
The post below has been deleted. Click to close.
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sadas123
1086 posts
sadas123
#4 h  Mar 19, 2025, 2:37 AM
Y by
I guess just make the tag again?
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
jkim0656
339 posts
jkim0656
#5 h  Mar 19, 2025, 3:58 AM
Y by
just write the tag and press enter
Z K Y
The post below has been deleted. Click to close.
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Zestra
424 posts
Zestra
#6 h  Mar 19, 2025, 4:27 AM
Y by
o.k.oo wrote:
The tag section for the question I shared is deleted after a while. What should not be done? Thanks.

the tag isn't deleted automatically after a while.
i think someone has replaced your tag,
so you need to correct it mangually
by creating a new tag like @bove
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