Problem

Source: Indian Postal Coaching 2012 Set 1 #4

Tags: geometry, combinatorics unsolved, combinatorics



Choose arbitrarily $n$ vertices of a regular $2n-$gon and colour them red. The remaining vertices are coloured 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.