red and blue vertices of a egular 2n-gon
Source: 2012 Romania JBMO TST 4.2, 10th Vojtech Jarnik Mathematical Competition, Ostrava, 2000
June 2, 2020
combinatorial geometrycombinatoricsColoring
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 nondecreasing sequence and do the same with the blue-blue distances. Prove that the two sequences thus obtained are identical.