Combinatorial Geometry show distances equal
Source: Indian Postal Coaching 2012 Set 1 #4
September 19, 2013
geometrycombinatorics unsolvedcombinatorics
Problem Statement
Choose arbitrarily vertices of a regular 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.