M2610

Part of Kvant 2020

Problems(1)

Vertices of a regular 100-gon are colored in 10 colors

Source: 2020 Caucasus Mathematical Olympiad

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.