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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]
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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
J
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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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PROM^2 for Girls 2025
mathisfun17   21
N a few seconds ago by Inaaya
Hi everyone!

The Princeton International School of Math and Science (PRISMS) Math Team is delighted that $PROM^2$ for Girls, PRISMS Online Math Meet for Girls, is happening this spring! https://www.prismsus.org/events/prom/home/index

We warmly invite all middle school girls to join us! This is a fantastic opportunity for young girls to connect with others interested in math as well as prepare for future math contests.

This contest will take place online from 12:00 pm to 3:00 pm EST on Saturday, April 26th, 2025.

The competition will include a team and individual round as well as activities like origami. You can see a detailed schedule here. https://prismsus.org/events/prom/experience/schedule.

Registration is FREE, there are cash prizes for participants who place in the top 10 and cool gifts for all participants.

1st place individual: $500 cash
2nd place individual: $300 cash
3rd place individual: $100 cash
4th-10th place individual: $50 cash each

Some FAQs:
Q: How difficult are the questions?
A: The problem difficulty is around AMC 8 or Mathcounts level.

Q: Are there any example problems?
A: You can find some archived here: https://www.prismsus.org/events/prom/achieve/achieve

Registration is open now. https://www.prismsus.org/events/prom/register/register. Email us at prom2@prismsus.org with any questions.

The PRISMS Peregrines Math Team welcomes you!
21 replies
mathisfun17
Feb 22, 2025
Inaaya
a few seconds ago
J
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Finding big a_i a_i+1
nAalniaOMliO   1
N 30 minutes ago by RagvaloD
Source: Belarusian National Olympiad 2025
Positive real numbers $a_1>a_2>\ldots>a_n$ with sum $s$ are such that the equation $nx^2-sx+1=0$ has a positive root $a_{n+1}$ smaller than $a_n$.
Prove that there exists a positive integer $r \leq n$ such that the inequality $a_ra_{r+1} \geq \frac{1}{r}$ holds.
1 reply
1 viewing
nAalniaOMliO
Friday at 8:36 PM
RagvaloD
30 minutes ago
J
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nice problem
hanzo.ei   2
N 35 minutes ago by Lil_flip38
Source: I forgot
Let triangle $ABC$ be inscribed in the circumcircle $(O)$ and circumscribed about the incircle $(I)$, with $AB < AC$. The incircle $(I)$ touches the sides $BC$, $CA$, and $AB$ at $D$, $E$, and $F$, respectively. A line through $I$, perpendicular to $AI$, intersects $BC$, $CA$, and $AB$ at $X$, $Y$, and $Z$, respectively. The line $AI$ meets $(O)$ at $M$ (distinct from $A$). The circumcircle of triangle $AYZ$ intersects $(O)$ at $N$ (distinct from $A$). Let $P$ be the midpoint of the arc $BAC$ of $(O)$. The line $AI$ cuts segments $DF$ and $DE$ at $K$ and $L$, respectively, and the tangents to the circle $(DKL)$ at $K$ and $L$ intersect at $T$. Prove that $AT \perp BC$.
2 replies
hanzo.ei
Yesterday at 5:58 PM
Lil_flip38
35 minutes ago
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Fixed point config on external similar isosceles triangles
Assassino9931   2
N 37 minutes ago by bin_sherlo
Source: Bulgaria Spring Mathematical Competition 2025 10.2
Let $AB$ be an acute scalene triangle. A point \( D \) varies on its side \( BC \). The points \( P \) and \( Q \) are the midpoints of the arcs \( \widehat{AB} \) and \( \widehat{AC} \) (not containing \( D \)) of the circumcircles of triangles \( ABD \) and \( ACD \), respectively. Prove that the circumcircle of triangle \( PQD \) passes through a fixed point, independent of the choice of \( D \) on \( BC \).
2 replies
Assassino9931
Today at 12:41 PM
bin_sherlo
37 minutes ago
J
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Fixed point as P varies
tenniskidperson3   86
N 44 minutes ago by ErTeeEs06
Source: 2016 USAJMO 1
The isosceles triangle $\triangle ABC$, with $AB=AC$, is inscribed in the circle $\omega$. Let $P$ be a variable point on the arc $\stackrel{\frown}{BC}$ that does not contain $A$, and let $I_B$ and $I_C$ denote the incenters of triangles $\triangle ABP$ and $\triangle ACP$, respectively.

Prove that as $P$ varies, the circumcircle of triangle $\triangle PI_BI_C$ passes through a fixed point.
86 replies
+1 w
tenniskidperson3
Apr 19, 2016
ErTeeEs06
44 minutes ago
J
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Colored Pencils for Math Competitions
Owinner   14
N an hour ago by BS2012
I've heard using colored pencils is really useful for geometry problems. Is this only for very hard problems, or can it be used in MATHCOUNTS/AMC 8/10? An example problem would be much appreciated.
14 replies
Owinner
Yesterday at 5:56 PM
BS2012
an hour ago
J
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9 Which math contest is your favorite?
mdk2013   4
N an hour ago by Andyluo
links for details on each comp

i think thats all the major ones, comment if you have any more that i forgot to include
upvote if you're like me and you think MATHCOUNTS is obv better!

EDIT: i forgot ARML and JBMO, comment if you like those
4 replies
mdk2013
an hour ago
Andyluo
an hour ago
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Question 2
Valentin Vornicu   87
N an hour ago by ItsBesi
Consider five points $ A$, $ B$, $ C$, $ D$ and $ E$ such that $ ABCD$ is a parallelogram and $ BCED$ is a cyclic quadrilateral. Let $ \ell$ be a line passing through $ A$. Suppose that $ \ell$ intersects the interior of the segment $ DC$ at $ F$ and intersects line $ BC$ at $ G$. Suppose also that $ EF = EG = EC$. Prove that $ \ell$ is the bisector of angle $ DAB$.

Author: Charles Leytem, Luxembourg
87 replies
Valentin Vornicu
Jul 25, 2007
ItsBesi
an hour ago
J
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Number theory
spiderman0   1
N an hour ago by MR.1
Find all n such that $3^n + 1$ is divisibly by $n^2$.
I want a solution that uses order or a solution like “let p be the least prime divisor of n”
1 reply
spiderman0
4 hours ago
MR.1
an hour ago
J
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Escape from the room
jannatiar   2
N an hour ago by sami1618
Source: 2024 AlborzMO P3
A person is locked in a room with a password-protected computer. If they enter the correct password, the door opens and they are freed. However, the password changes every time it is entered incorrectly. The person knows that the password is always a 10-digit number, and they also know that the password change follows a fixed pattern. This means that if the current password is \( b \) and \( a \) is entered, the new password is \( c \), which is determined by \( b \) and \( a \) (naturally, the person does not know \( c \) or \( b \)). Prove that regardless of the characteristics of this computer, the prisoner can free themselves.

Proposed by Reza Tahernejad Karizi
2 replies
jannatiar
Mar 4, 2025
sami1618
an hour ago
J
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Midpoints of chords on a circle
AwesomeToad   38
N 2 hours ago by LeYohan
Source: 0
Let $C$ be a circle and $P$ a given point in the plane. Each line through $P$ which intersects $C$ determines a chord of $C$. Show that the midpoints of these chords lie on a circle.
38 replies
AwesomeToad
Sep 23, 2011
LeYohan
2 hours ago
J
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Polish MO finals, problem 1
michaj   4
N 2 hours ago by AshAuktober
In each cell of a matrix $ n\times n$ a number from a set $ \{1,2,\ldots,n^2\}$ is written --- in the first row numbers $ 1,2,\ldots,n$, in the second $ n+1,n+2,\ldots,2n$ and so on. Exactly $ n$ of them have been chosen, no two from the same row or the same column. Let us denote by $ a_i$ a number chosen from row number $ i$. Show that:

\[ \frac{1^2}{a_1}+\frac{2^2}{a_2}+\ldots +\frac{n^2}{a_n}\geq \frac{n+2}{2}-\frac{1}{n^2+1}\]
4 replies
michaj
Apr 10, 2008
AshAuktober
2 hours ago
J
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2025 Caucasus MO Seniors P7
BR1F1SZ   1
N 2 hours ago by X.Luser
Source: Caucasus MO
From a point $O$ lying outside the circle $\omega$, two tangents are drawn touching $\omega$ at points $M$ and $N$. A point $K$ is chosen on the segment $MN$. Let points $P$ and $Q$ be the midpoints of segments $KM$ and $OM$ respectively. The circumcircle of triangle $MPQ$ intersects $\omega$ again at point $L$ ($L \neq M$). Prove that the line $LN$ passes through the centroid of triangle $KMO$.
1 reply
BR1F1SZ
Mar 26, 2025
X.Luser
2 hours ago
J
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Easy geometry
Bluesoul   13
N 2 hours ago by AshAuktober
Source: CJMO 2022 P1
Let $\triangle{ABC}$ has circumcircle $\Gamma$, drop the perpendicular line from $A$ to $BC$ and meet $\Gamma$ at point $D$, similarly, altitude from $B$ to $AC$ meets $\Gamma$ at $E$. Prove that if $AB=DE, \angle{ACB}=60^{\circ}$
(sorry it is from my memory I can't remember the exact problem, but it means the same)
13 replies
Bluesoul
Mar 12, 2022
AshAuktober
2 hours ago
J
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J
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Pascal, Cayley and Fermat 2025
melpomene7   50
N Yesterday at 12:56 PM by Cerberusman
Anyone else do a CEMC contest? I did fermat but totally fumbled and got a 108.
50 replies
melpomene7
Feb 28, 2025
Cerberusman
Yesterday at 12:56 PM
J
Pascal, Cayley and Fermat 2025
G H J
Reveal topic tags
Fermat
Cayley
Pascal
CEMC
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G H BBookmark kLocked kLocked NReply
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melpomene7
4 posts
melpomene7
#1 h  Feb 28, 2025, 3:27 PM
Y by
Anyone else do a CEMC contest? I did fermat but totally fumbled and got a 108.
This post has been edited 1 time. Last edited by melpomene7, Feb 28, 2025, 4:09 PM
Reason: Grammar
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MathCosine
126 posts
MathCosine
#2 h  Feb 28, 2025, 4:38 PM
Y by
I took the Pascal. Are we allowed to discuss the questions now?
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melpomene7
4 posts
melpomene7
#3 h  Feb 28, 2025, 4:41 PM
Y by
Yes, it's been 48 hours.
Z K Y
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MathCosine
126 posts
MathCosine
#4 h  Feb 28, 2025, 4:46 PM
Y by
For the last 5 on the Pascal, what did we get? my approaches
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Iwowowl253
120 posts
Iwowowl253
#5 h  Feb 28, 2025, 9:28 PM
Y by
My Answers For The Last 5(Pascal)
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Squidget
433 posts
Squidget
#6 h  Feb 28, 2025, 9:36 PM
Y by
My answers for the last 5(pascal
Predicted 134 because I forgot how to count on question 20.
Was it just me or was it easier this year?
This post has been edited 4 times. Last edited by Squidget, Feb 28, 2025, 9:39 PM
Reason: Formatting
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MathCosine
126 posts
MathCosine
#7 h  Feb 28, 2025, 11:05 PM
Y by
Iwowowl253 wrote:
My Answers For The Last 5(Pascal)

Wait i agree but for question 24 I got 23 like Squidget????
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Iwowowl253
120 posts
Iwowowl253
#8 h  Mar 1, 2025, 12:29 AM
Y by
MathCosine wrote:
Iwowowl253 wrote:
My Answers For The Last 5(Pascal)

Wait i agree but for question 24 I got 23 like Squidget????

Yeah nvm that’s probably right. Welp, no full score…
Z K Y
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Jeffreyscb
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Jeffreyscb
#9 h  Mar 3, 2025, 6:34 PM
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anyone did fermat?

My answers for fermat last 5
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Disjunction
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Disjunction
#10 h  Mar 8, 2025, 3:03 AM
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I did Pascal; I don't remember my answers, but I got 133/150 in the best case.
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Disjunction
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Disjunction
#11 h  Mar 8, 2025, 3:05 AM
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Squidget wrote:
My answers for the last 5(pascal
Predicted 134 because I forgot how to count on question 20.
Was it just me or was it easier this year?

I agree with the answers for 21 and 22; I don't remember the rest.

It was a lot easier this year I think.
This post has been edited 1 time. Last edited by Disjunction, Mar 8, 2025, 3:06 AM
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MathCosine
126 posts
MathCosine
#12 h  Mar 8, 2025, 3:06 AM
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Does anyone know when the official answers + cutoffs will be released?
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stjwyl
1250 posts
stjwyl
#13 h  Mar 8, 2025, 3:06 AM
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what grades are pascal cayley and fermat again
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Disjunction
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Disjunction
#14 h  Mar 8, 2025, 3:07 AM
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MathCosine wrote:
Does anyone know when the official answers + cutoffs will be released?

I got told sometime in (early) Spring.
BTW, any of y'all looking forward to the other contests by uWaterloo? If so, would anyone be interested in prepping together?
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Disjunction
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Disjunction
#15 h  Mar 8, 2025, 3:07 AM
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stjwyl wrote:
what grades are pascal cayley and fermat again

9, 10, 11
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