MathDB

2

Part of 2020 Serbia National Math Olympiad

Problems(1)

Combinatorial geometry with polyhedra

Source: 2020 Serbian MO, Problem 2

9/26/2020
We are given a polyhedron with at least 55 vertices, such that exactly 33 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:
(i)(i) At least one of the numbers assigned to the vertices is equal to 20202020.
(ii)(ii) For every polygonal face, the product of the numbers assigned to the vertices of that face is equal to 11.
geometrycombinatorics