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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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0 replies
jlacosta
3 hours ago
0 replies
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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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A property of divisors
rightways   10
N 4 minutes ago by akliu
Source: Kazakhstan NMO 2016, P1
Prove that one can arrange all positive divisors of any given positive integer around a circle so that for any two neighboring numbers one is divisible by another.
10 replies
rightways
Mar 17, 2016
akliu
4 minutes ago
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Famous geo configuration appears on the district MO
AndreiVila   3
N 16 minutes 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
16 minutes ago
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kind of well known?
dotscom26   2
N 18 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
18 minutes ago
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hard problem
Cobedangiu   0
19 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
19 minutes ago
0 replies
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No more topics!
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Concyclic points
GGPiku   1
N Nov 18, 2017 by MathGan
Source: IMAR 2017, Problem 1
Let $P$ be a point in the interior $\triangle ABC$, and $AD,BE,CF$ 3 concurrent cevians through $P$, with $D,E,F$ on $BC,CA,AB$. The circle with the diameter $BC$ intersects the circle with the diameter $AD$ in $D_1,D_2$. Analogously we define $E_1,E_2$ and $F_1,F_2$. Prove that $D_1,D_2,E_1,E_2,F_1,F_2$ are concylic.
1 reply
GGPiku
Nov 18, 2017
MathGan
Nov 18, 2017
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Concyclic points
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Reveal topic tags
geometry
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Source: IMAR 2017, Problem 1
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GGPiku
402 posts
GGPiku
#1 h  Nov 18, 2017, 7:47 PM • 1 Y
Y by Adventure10
Let $P$ be a point in the interior $\triangle ABC$, and $AD,BE,CF$ 3 concurrent cevians through $P$, with $D,E,F$ on $BC,CA,AB$. The circle with the diameter $BC$ intersects the circle with the diameter $AD$ in $D_1,D_2$. Analogously we define $E_1,E_2$ and $F_1,F_2$. Prove that $D_1,D_2,E_1,E_2,F_1,F_2$ are concylic.
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MathGan
68 posts
MathGan
#2 h  Nov 18, 2017, 8:08 PM • 2 Y
Y by Adventure10, Mango247
see here

https://artofproblemsolving.com/community/q2h1213623p6028184
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