polyhedron with n faces
Source: Romanian ROM TST 2004, problem 15, created by Calin Popescu
May 24, 2004
Eulercombinatorics solvedcombinatorics
Problem Statement
Some of the faces of a polyhedron are colored in black such that any two black-colored faces have no common vertex. The rest of the faces of the polyhedron are colored in white.
Prove that the number of common sides of two white-colored faces of the polyhedron is at least .