Question 2
A pentagonal prism $A_1A_2\ldots A_5B_1B_2\ldots B_5$ is given. The edges, the diagonals of the lateral walls and the internal diagonals of the prism are each colored either red or green in such a way that no triangle whose vertices are vertices of the prism has its three edges of the same color. Prove that all edges of the bases are of the same color.