Vertices of a regular 100-gon are colored in 10 colors
Source: 2020 Caucasus Mathematical Olympiad
March 16, 2020
combinatorics
Problem Statement
All vertices of a regular 100-gon are colored in 10 colors. Prove that there exist 4 vertices of the given 100-gon which are the vertices of a rectangle and which are colored in at most 2 colors.