MathDB
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 nn 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 nāˆ’2n-2.