equal sums of colored areas, spherw inscribed in convex polyhedron
Source: Polish MO Second Round 1975 p5
September 8, 2024
geometry3D geometryColoringcombinatorial geometry
Problem Statement
Prove that if a sphere can be inscribed in a convex polyhedron and each face of this polyhedron can be painted in one of two colors such that any two faces sharing a common edge are of different colors, then the sum of the areas of the faces of one color is equal to the sum of the areas of the faces of the other color.