painting the faces of an icosahedron into 5 colors ...
Source: 2015 Sharygin Geometry Olympiad Correspondence Round P22
August 2, 2018
combinatoricscombinatorial geometryColoring
Problem Statement
The faces of an icosahedron are painted into colors in such a way that two faces painted into the same color have no common points, even a vertices. Prove that for any point lying inside the icosahedron the sums of the distances from this point to the red faces and the blue faces are equal.