OME 2015 Problem 4

All faces of a polyhedron are triangles. Each of the vertices of this polyhedron is assigned independently one of three colors : green, white or black. We say that a face is Extremadura if its three vertices are of different colors, one green, one white and one black. Is it true that regardless of how the vertices's color, the number of Extremadura faces of this polyhedron is always even?