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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
3 hours ago
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 16th (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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jlacosta
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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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Famous geo configuration appears on the district MO
AndreiVila   3
N a minute ago by chirita.andrei
Source: Romanian District Olympiad 2025 10.4
Let $ABCDEF$ be a convex hexagon with $\angle A = \angle C=\angle E$ and $\angle B = \angle D=\angle F$.
[list=a]
[*] Prove that there is a unique point $P$ which is equidistant from sides $AB,CD$ and $EF$.
[*] If $G_1$ and $G_2$ are the centers of mass of $\triangle ACE$ and $\triangle BDF$, show that $\angle G_1PG_2=60^{\circ}$.
3 replies
AndreiVila
Mar 8, 2025
chirita.andrei
a minute ago
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kind of well known?
dotscom26   2
N 3 minutes ago by alexheinis
Source: MBL
Let $ y_1, y_2, ..., y_{2025}$ be real numbers satisfying
$ y_1^2 + y_2^2 + \cdots + y_{2025}^2 = 1. $
Find the maximum value of
$ |y_1 - y_2| + |y_2 - y_3| + \cdots + |y_{2025} - y_1|. $

I have seen many problems with the same structure, Id really appreciate if someone could explain which approach is suitable here
2 replies
dotscom26
Yesterday at 4:11 AM
alexheinis
3 minutes ago
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hard problem
Cobedangiu   0
4 minutes ago
Let $x,y,z>0$ and $xy+yz+zx=3$ : Prove that :
$\sum \ \frac{x}{y+z}\ge\sum \frac{1}{\sqrt{x+3}}$
0 replies
Cobedangiu
4 minutes ago
0 replies
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Ornaments and Christmas trees
Morskow   30
N 8 minutes ago by akliu
Source: Slovenia IMO TST 2018, Day 1, Problem 1
Let $n$ be a positive integer. On the table, we have $n^2$ ornaments in $n$ different colours, not necessarily $n$ of each colour. Prove that we can hang the ornaments on $n$ Christmas trees in such a way that there are exactly $n$ ornaments on each tree and the ornaments on every tree are of at most $2$ different colours.
30 replies
+1 w
Morskow
Dec 17, 2017
akliu
8 minutes ago
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No more topics!
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2006 BMO1 P2 (Geometry)
maplestory   6
N Oct 27, 2012 by maplestory
In the convex quadrilateral $ABCD$, points $M,N$ lie on $\overline{AB}$ such that $AM = MN = NB$, and points $P,Q$ lie on the $\overline{CD}$ such that $CP = PQ = QD$. Prove that $[AMCP] = [MNPQ] =\frac{1}{3}[ABCD]$.
6 replies
maplestory
Oct 27, 2012
maplestory
Oct 27, 2012
J
2006 BMO1 P2 (Geometry)
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Reveal topic tags
geometry
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maplestory
1458 posts
maplestory
#1 h  Oct 27, 2012, 10:05 PM • 2 Y
Y by Adventure10, Mango247
In the convex quadrilateral $ABCD$, points $M,N$ lie on $\overline{AB}$ such that $AM = MN = NB$, and points $P,Q$ lie on the $\overline{CD}$ such that $CP = PQ = QD$. Prove that $[AMCP] = [MNPQ] =\frac{1}{3}[ABCD]$.
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Farenhajt
5167 posts
Farenhajt
#2 h  Oct 27, 2012, 10:29 PM • 1 Y
Y by Adventure10
$[ACP]={1\over 3}[ACD]\land [AMC]={1\over 3}[ABC]$. Add them up to get $[AMCP]={1\over 3}[ABCD]$

Similar proof for $[BQDN]={1\over 3}[ABCD]$.

And what remains at the end is $[MNPQ]$.
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maplestory
1458 posts
maplestory
#3 h  Oct 27, 2012, 10:34 PM • 1 Y
Y by Adventure10
What does the arrow symbol pointing upwards represent?

Thanks
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Farenhajt
5167 posts
Farenhajt
#4 h  Oct 27, 2012, 10:38 PM • 1 Y
Y by Adventure10
You mean this: $\land$?
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maplestory
1458 posts
maplestory
#5 h  Oct 27, 2012, 10:41 PM • 1 Y
Y by Adventure10
Yep that one
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Farenhajt
5167 posts
Farenhajt
#6 h  Oct 27, 2012, 10:43 PM • 2 Y
Y by maplestory, Adventure10
It means "and". This one: $\lor$ - means "or".
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maplestory
1458 posts
maplestory
#7 h  Oct 27, 2012, 10:48 PM • 1 Y
Y by Adventure10
Thanks I understand the solution now.
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