Anton the ant walks along the vertices of a cube, each but 1 vertice once
Source: Flanders Math Olympiad 2013 p3
December 24, 2022
combinatoricscombinatorial geometrycube
Problem Statement
Anton the ant takes a walk along the vertices of a cube. He starts at a vertex and stops when it reaches this point again. Between two vertices it moves over an edge, a side face diagonal or a space diagonal. During the rout it visits each of the other vertices exactly once and nowhere intersects its road already traveled.
(a) Show that Anton walks along at least one edge.
(b) Show that Anton walks along at least two edges.