Question

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∈{1,…,30} and a y∈{1,…,30}. Of the 900 different possible starting positions for the token, how many positions result in a guaranteed winning strategy for the first player?