Every edge of a regular dodecahedron is assigned a number from We use each number exactly once. Determine whether it is possible to do it in such way that the sum of edges that come out of every vertex is (a) even; (b) divisible by 4.
For (a), I figured that among the three edges that come out of each vertex, either all must be even, or one even and two odd. So instead of assigning number, I just try to color the edges on the net of a dodecahedron with two colors, say black and red, where red = odd number, so that every vertex has two red edges or no red edges, and that there are 15 red edges in total. But I have trouble arriving at the final solution.
Your help will be appreciated.