RMM 2013 Problem 6
Source:
March 3, 2013
geometrygeometric transformationreflectioncombinatorics
Problem Statement
A token is placed at each vertex of a regular -gon. A move consists in choosing an edge of the -gon and swapping the two tokens placed at the endpoints of that edge. After a finite number of moves have been performed, it turns out that every two tokens have been swapped exactly once. Prove that some edge has never been chosen.