Flies on a cube
Source: Centroamerican 2011, Problem 1
June 22, 2011
geometry3D geometrycountingderangementcombinatorics proposedcombinatorics
Problem Statement
Consider a cube with a fly standing at each of its vertices. When a whistle blows, each fly moves to a vertex in the same face as the previous one but diagonally opposite to it. After the whistle blows, in how many ways can the flies change position so that there is no vertex with 2 or more flies?