thanks~~

[text deleted]

From the moderator: It is inadvisable to explain solutions of difficult problems. I have the right to delete such explanations.

Edited by moderator 25.06.2006 23:01

I'll post my hint because it is a general approach and common theory rather than a solution for this particular problem.

For 3D primitives there is Euler formula v+f-e=2 where 'v' is number of vertices, 'f' is number of faces and 'e' is number of edges (plus/minus is easy to memorize via parallelepiped, v=8, f=6, e=12, so only v+f-e=2 gives the right answer).

This formula also applies to planar graphs in the form v+f-e-c=1 where 'c' is number of connected components, and outer face of planar graph is also counted.