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k a My Retirement & New Leadership at AoPS
rrusczyk   1571
N Mar 26, 2025 by SmartGroot
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
1571 replies
rrusczyk
Mar 24, 2025
SmartGroot
Mar 26, 2025
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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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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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Classic complex number geo
Ciobi_   0
a minute ago
Source: Romania NMO 2025 10.1
Let $M$ be a point in the plane, distinct from the vertices of $\triangle ABC$. Consider $N,P,Q$ the reflections of $M$ with respect to lines $AB, BC$ and $CA$, in this order.
a) Prove that $N, P ,Q$ are collinear if and only if $M$ lies on the circumcircle of $\triangle ABC$.
b) If $M$ does not lie on the circumcircle of $\triangle ABC$ and the centroids of triangles $\triangle ABC$ and $\triangle NPQ$ coincide, prove that $\triangle ABC$ is equilateral.
0 replies
Ciobi_
a minute ago
0 replies
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Is this FE solvable?
Mathdreams   1
N 2 minutes ago by pco
Find all $f:\mathbb{R} \rightarrow \mathbb{R}$ such that \[f(2x+y) + f(x+f(2y)) = f(x)f(y) - xy\]for all reals $x$ and $y$.
1 reply
Mathdreams
Yesterday at 6:58 PM
pco
2 minutes ago
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Proving 2 sequences are bounded above
Ciobi_   0
9 minutes ago
Source: Romania NMO 2025 9.4
Let $m \geq 2$ be a fixed positive integer, and $(a_n)_{n\geq 1}$ be a sequence of nonnegative real numbers such that, for all $n\geq 1$, we have that $a_{n+1} \leq a_n - a_{mn}$.
a) Prove that the sequence $b_n = \sum_{k=1}^{n} a_k$ is bounded above.
b) Prove that the sequence $c_n = \sum_{k=1}^{n} k^2 a_k$ is bounded above.
0 replies
Ciobi_
9 minutes ago
0 replies
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One nice inequlity 1
prof.   1
N 17 minutes ago by sqing
If $a,b,c$ are positiv real number, such that $a^2+b^2+c^2=3abc$ prove inequality $$\frac{a}{b^2c^2}+\frac{b}{c^2a^2}+\frac{c}{a^2b^2}\ge\frac{9}{a+b+c}.$$
1 reply
prof.
42 minutes ago
sqing
17 minutes ago
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Bounding number of solutions for floor function equation
Ciobi_   0
19 minutes ago
Source: Romania NMO 2025 9.3
Let $n \geq 2$ be a positive integer. Consider the following equation: \[ \{x\}+\{2x\}+ \dots + \{nx\} = \lfloor x \rfloor + \lfloor 2x \rfloor + \dots + \lfloor 2nx \rfloor\]a) For $n=2$, solve the given equation in $\mathbb{R}$.
b) Prove that, for any $n \geq 2$, the equation has at most $2$ real solutions.
0 replies
Ciobi_
19 minutes ago
0 replies
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Olympiad Geometry problem-second time posting
kjhgyuio   3
N 20 minutes ago by kjhgyuio
Source: smo problem
In trapezium ABCD,AD is parallel to BC and points E and F are midpoints of AB and DC respectively. If
Area of AEFD/Area of EBCF =√3 + 1/3-√3 and the area of triangle ABD is √3 .find the area of trapezium ABCD
3 replies
kjhgyuio
Today at 1:03 AM
kjhgyuio
20 minutes ago
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Sequel to IMO 2016/1
Scilyse   6
N 23 minutes ago by L13832
Source: 2024 MODS Geometry Contest, Problem 4 of 6
Let $ABCD$ be a parallelogram. Let line $\ell$ externally bisect $\angle DCA$ and let $\ell'$ be the line passing through $D$ which is parallel to line $AC$. Suppose that $\ell'$ meets line $AB$ at point $E$ and $\ell$ at point $F$, and that $\ell$ meets the internal bisector of $\angle BAC$ at point $X$. Further let circle $EXF$ meet line $BX$ at point $Y \neq X$ and the internal bisector of $\angle DCA$ meet circle $AXC$ at point $Z \neq C$.
Prove that points $D$, $X$, $Y$, and $Z$ are concyclic.

Proposed by squarc_rs3v2m
6 replies
Scilyse
Mar 15, 2024
L13832
23 minutes ago
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2 var inquality
sqing   1
N 24 minutes ago by sqing
Source: Own
Let $ a,b\geq 0 $ and $ 2a+2b+ab=5 $. Prove that
$$\frac{1}{a+1}+\frac{1}{b+1}+ \frac{1}{a+b}+\frac{9ab}{20(a+b+ab)} \geq \frac{33}{20}$$$$\frac{1}{a+1}+\frac{1}{b+1}+ \frac{1}{a+b}+\frac{31ab}{50(a+b+ab)} \geq \frac{59}{35}$$$$\frac{1}{a+1}+\frac{1}{b+1}+ \frac{1}{a+b}+\frac{0.616327 ab}{a+b+ab} \geq \frac{59}{35}$$
1 reply
1 viewing
sqing
an hour ago
sqing
24 minutes ago
J
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Vector geometry with unusual points
Ciobi_   0
30 minutes ago
Source: Romania NMO 2025 9.2
Let $\triangle ABC$ be an acute-angled triangle, with circumcenter $O$, circumradius $R$ and orthocenter $H$. Let $A_1$ be a point on $BC$ such that $A_1H+A_1O=R$. Define $B_1$ and $C_1$ similarly.
If $\overrightarrow{AA_1} + \overrightarrow{BB_1} + \overrightarrow{CC_1} = \overrightarrow{0}$, prove that $\triangle ABC$ is equilateral.
0 replies
Ciobi_
30 minutes ago
0 replies
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9 Olympiad question poll
kjhgyuio   0
31 minutes ago
evaluate without calculator
0 replies
kjhgyuio
31 minutes ago
0 replies
J
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Procedure involving colored numbers
Ciobi_   0
40 minutes ago
Source: Romania NMO 2025 9.1
Let $N \geq 1$ be a positive integer. There are two numbers written on a blackboard, one red and one blue. Initially, both are 0. We define the following procedure: at each step, we choose a nonnegative integer $k$ (not necessarily distinct from the previously chosen ones), and, if the red and blue numbers are $x$ and $y$ respectively, we replace them with $x+k+1$ and $y+k^2+2$, which we color blue and red (in this order). We keep doing this procedure until the blue number is at least $N$.
Determine the minimum value of the red number at the end of this procedure.
0 replies
Ciobi_
40 minutes ago
0 replies
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Poland Inequalities
wangzishan   6
N an hour ago by AshAuktober
Leta,b,c are postive real numbers,proof that $ \frac{a}{b+2c}+\frac{b}{c+2a}+\frac{c}{a+2b}\geq1$
6 replies
wangzishan
Apr 23, 2009
AshAuktober
an hour ago
J
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A cyclic inequality
KhuongTrang   0
an hour ago
Source: own-CRUX
IMAGE
Link
0 replies
KhuongTrang
an hour ago
0 replies
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Image of f(a + b) - f(a) - f(b)
RootofUnityfilter   0
an hour ago
Source: my teacher
Let $\mathbb{Z}_{>0}$ be the set of all positive integers. Determine all subsets $\mathcal{S}$ of $\{2^0, 2^1, 2^2, \dots\}$ such that
$$\mathcal{S} = \{f(a + b) - f(a) - f(b) | a, b \in \mathbb{Z}_{>0}\}$$
0 replies
RootofUnityfilter
an hour ago
0 replies
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Regular hexagon
MinatoF   1
N Oct 18, 2012 by Luis González
Source: JBMO 2005 Shortlist
Let $ABCDEF$ be a regular hexagon and $M\in (DE)$, $N\in(CD)$ such that $m (\widehat {AMN}) = 90^\circ$ and $AN = CM \sqrt {2}$. Find the value of $\frac{DM}{ME}$.
1 reply
MinatoF
Oct 17, 2012
Luis González
Oct 18, 2012
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Regular hexagon
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Reveal topic tags
geometry
circumcircle
trigonometry
angle bisector
geometry unsolved
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Source: JBMO 2005 Shortlist
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MinatoF
131 posts
MinatoF
#1 h  Oct 17, 2012, 9:36 PM • 4 Y
Y by parmenides51, Adventure10, Mango247, and 1 other user
Let $ABCDEF$ be a regular hexagon and $M\in (DE)$, $N\in(CD)$ such that $m (\widehat {AMN}) = 90^\circ$ and $AN = CM \sqrt {2}$. Find the value of $\frac{DM}{ME}$.
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The post below has been deleted. Click to close.
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Luis González
4145 posts
Luis González
#2 h  Oct 18, 2012, 1:05 AM • 3 Y
Y by MinatoF, Adventure10, Mango247
Since $\widehat{AMN}=\widehat{ACN}=90^{\circ},$ then $AN$ is a diameter of the circumcircle of $\triangle ACM$ $\Longrightarrow$ $CM=AN \cdot \sin \widehat{MAC}$ $\Longrightarrow$ $\sin \widehat{MAC}=\frac{_1}{^{\sqrt{2}}}$ $\Longrightarrow$ $\widehat{MAC}=45^{\circ},$ since $\widehat{MAC} < 60^{\circ}.$ Thus $\widehat{EAM}=60^{\circ}-45^{\circ}=15^{\circ}$ $\Longrightarrow$ $AM$ bisects $\widehat{DAE}.$ By angle bisector theorem on $\triangle DAE,$ we have then

$\frac{DM}{ME}=\frac{DA}{AE}=\frac{\frac{2\sqrt{3}}{3}AE}{AE}=\frac{2\sqrt{3}}{3}.$
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