Combinatorial geometry with polyhedra
Source: 2020 Serbian MO, Problem 2
September 26, 2020
geometrycombinatorics
Problem Statement
We are given a polyhedron with at least vertices, such that exactly edges meet in each of the vertices. Prove that we can assign a rational number to every vertex of the given polyhedron such that the following conditions are met: At least one of the numbers assigned to the vertices is equal to . For every polygonal face, the product of the numbers assigned to the vertices of that face is equal to .