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**fifthrapiers** Suppose a queen starts out standing on the third square on a chessboard at the very top. That is, the queen stands on the 3rd sqaure from the left. Two players play a game where each player takes a turn moving the queen:

a.) either horizontally to the right

b.) or vertically downward

c.) or diagonally in south-east direction

For the above, they can move the queen as many squares as they want.

The first player that can place the queen on the lower-left most right square of the chessboard wins the game.

Who will win, and what is the winning strategy for each n and m?