ICMC 2018/19 Round 2, Problem 1
Source: Imperial College Mathematics Competition 2018/19 - Round 2
August 7, 2020
college contests
Problem Statement
Observe that, in the usual chessboard colouring of the two-dimensional grid, each square has 4 of its 8 neighbours black and 4 white. Does there exist a way to colour the three-dimensional grid such that each cube has half of its 26 neighbours black and half white? Is this possible in four dimensions?