Covering
Source: Tuymaada 2016, Senior P2, Junior P3
July 22, 2016
combinatorics
Problem Statement
A cube stands on one of the squares of an infinite chessboard.
On each face of the cube there is an arrow pointing in one of the four directions
parallel to the sides of the face. Anton looks on the cube from above and
rolls it over an edge in the direction pointed by the arrow on the top face.
Prove that the cube cannot cover any square.