2
Part of 2002 Putnam
Problems(2)
Putnam 2002 A2
Source:
3/12/2012
Given any five points on a sphere, show that some four of them must lie on a closed hemisphere.
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Putnam 2002 B2
Source:
3/12/2012
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.
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