The vertices of a prism are colored using two colors, so that each lateral edge has its vertices differently colored. Consider all the segments that join vertices of the prism and are not lateral edges. Prove that the number of such segments with endpoints differently colored is equal to the number of such segments with endpoints of the same color.
Problem
Source: 2016 Romanian NMO grade VIII P1
Tags: geometry, 3D geometry, prism, combinatorics, combinatorial geometry, Coloring