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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
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
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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 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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Nationalist Combo
blacksheep2003   15
N 5 minutes ago by cj13609517288
Source: USEMO 2019 Problem 5
Let $\mathcal{P}$ be a regular polygon, and let $\mathcal{V}$ be its set of vertices. Each point in $\mathcal{V}$ is colored red, white, or blue. A subset of $\mathcal{V}$ is patriotic if it contains an equal number of points of each color, and a side of $\mathcal{P}$ is dazzling if its endpoints are of different colors.

Suppose that $\mathcal{V}$ is patriotic and the number of dazzling edges of $\mathcal{P}$ is even. Prove that there exists a line, not passing through any point in $\mathcal{V}$, dividing $\mathcal{V}$ into two nonempty patriotic subsets.

Ankan Bhattacharya
15 replies
blacksheep2003
May 24, 2020
cj13609517288
5 minutes ago
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Concurrency with 10 lines
oVlad   1
N 18 minutes ago by kokcio
Source: Romania EGMO TST 2017 Day 1 P1
Consider five points on a circle. For every three of them, we draw the perpendicular from the centroid of the triangle they determine to the line through the remaining two points. Prove that the ten lines thus formed are concurrent.
1 reply
oVlad
4 hours ago
kokcio
18 minutes ago
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Advanced topics in Inequalities
va2010   21
N 21 minutes ago by Novmath
So a while ago, I compiled some tricks on inequalities. You are welcome to post solutions below!
21 replies
va2010
Mar 7, 2015
Novmath
21 minutes ago
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GCD of a sequence
oVlad   1
N 27 minutes ago by kokcio
Source: Romania EGMO TST 2017 Day 1 P2
Determine all pairs $(a,b)$ of positive integers with the following property: all of the terms of the sequence $(a^n+b^n+1)_{n\geqslant 1}$ have a greatest common divisor $d>1.$
1 reply
+2 w
oVlad
4 hours ago
kokcio
27 minutes ago
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Tedious Whiteboard Process
KHOMNYO2   0
Apr 15, 2025
Tony writes $2018$ consecutive natural numbers starting from $1, 2, \dots, 2018$ on whiteboard. Every minutes, he will erase $4$ numbers (not necessary different), in the form of $(x,y,z,x+y+z)$ and write $3$ numbers back on the whiteboard in the form of $(x+y,y+z,z+x)$. Tony will stop whenever he cannot erase any 4 numbers that satisfy the condition anymore. If let's say, Tony starts at $08:00$ (8 AM), prove that Tony will stop before $16:30$ (4.30 PM)
0 replies
KHOMNYO2
Apr 15, 2025
0 replies
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Tedious Whiteboard Process
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KHOMNYO2
#1 h  Apr 15, 2025, 10:34 AM
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Tony writes $2018$ consecutive natural numbers starting from $1, 2, \dots, 2018$ on whiteboard. Every minutes, he will erase $4$ numbers (not necessary different), in the form of $(x,y,z,x+y+z)$ and write $3$ numbers back on the whiteboard in the form of $(x+y,y+z,z+x)$. Tony will stop whenever he cannot erase any 4 numbers that satisfy the condition anymore. If let's say, Tony starts at $08:00$ (8 AM), prove that Tony will stop before $16:30$ (4.30 PM)
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