MathDB
Putnam 2013 A1

Source:

December 9, 2013
Putnamgeometry3D geometryicosahedronprobabilityexpected valuecollege contests

Problem Statement

Recall that a regular icosahedron is a convex polyhedron having 12 vertices and 20 faces; the faces are congruent equilateral triangles. On each face of a regular icosahedron is written a nonnegative integer such that the sum of all 2020 integers is 39.39. Show that there are two faces that share a vertex and have the same integer written on them.