# Game of Life is not fair

**Discrete Mathematics**Level 5

Two players play a game on the Cartesian plane. The game starts by placing a token at a lattice point in the first quadrant. The players alternate turns, with player one going first. On her turn, player 1 can move the token 2 units to the left or 1 unit down. On his turn, player 2 can move the token 1 unit to the left or 2 units down. A player loses the game if s/he makes either co-ordinate of the token negative. The starting position of the token is determined by randomly choosing an \(x \in \{1,\ldots,30\}\) and a \(y \in \{1,\ldots,30\}\). Of the 900 different possible starting positions for the token, how many positions result in a guaranteed winning strategy for the first player?

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