2-coloring 2n-gon, sequence of side lengths are equal
Source: VJIMC 2000 1.4
July 27, 2021
geometry
Problem Statement
Let us choose arbitrarily vertices of a regular -gon and color them red. The remaining vertices are colored blue. We arrange all red-red distances into a non-decreasing sequence and do the same with the blue-blue distances. Prove that the sequences are equal.