This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2002 Putnam, 2
Tags: tetrahedron , geometry , 3d geometry , euler , putnam games
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.

2002 Putnam, 4
Tags: linear algebra , matrix , symmetry , putnam games
In Determinant Tic-Tac-Toe, Player $1$ enters a $1$ in an empty $3 \times 3$ matrix. Player $0$ counters with a $0$ in a vacant position and play continues in turn intil the $ 3 \times 3 $ matrix is completed with five $1$’s and four $0$’s. Player $0$ wins if the determinant is $0$ and player $1$ wins otherwise. Assuming both players pursue optimal strategies, who will win and how?