Problem #PRU-31087

Problems Algebra and arithmetic Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other) Calculus Real numbers Integer and fractional parts. Archimedean property
 12–14  2.0

Problem

The faces of a polyhedron are coloured in two colours so that the neighbouring faces are of different colours. It is known that all of the faces except for one have a number of edges that is a multiple of 3. Prove that this one face has a multiple of 3 edges.