Problem

Source: Peru IMO TST 2018 p8

Tags: Coloring, Color problem, dodecahedron, combinatorics, geometry, 3D geometry



You want to paint some edges of a regular dodecahedron red so that each face has an even number of painted edges (which can be zero). Determine from How many ways this coloration can be done. Note: A regular dodecahedron has twelve pentagonal faces and in each vertex concur three edges. The edges of the dodecahedron are all different for the purpose of the coloring . In this way, two colorings are the same only if the painted edges they are the same.