Putnam 2002 B2
Source:
March 12, 2012
Putnamgeometry3D geometrytetrahedronEulercollege contestsPutnam games
Problem Statement
Consider a polyhedron with at least five faces such that exactly three edges emerge from each of its vertices. Two players play the following game: Each, in turn, signs his or her name on a previously unsigned face. The winner is the player who first succeeds in signing three faces that share a common vertex. Show that the player who signs first will always win by playing as well as possible.