coloring unit cubes inside a parallelepiped of dimension a x b x c
Source: Bulgaria 2009 NMO p3
May 28, 2019
combinatoricsparallelepipedColoringColor problem
Problem Statement
Through the points with integer coordinates in the right-angled coordinate system are constructed planes, parallel to the coordinate planes and in this way the space is divided to unit cubes. Find all triples () consisting of natural numbers () for which the cubes formed can be coloured in colors in such a way that every palellepiped with dimensions a \times b \times c, having vertices with integer coordinates and sides parallel to the coordinate axis doesn't contain unit cubes in the same color.