It is said the following problem was posed (or solved?) by Zermelo. I'm not sure about that. I read it in an economic forum. But no one gives an answer there!

m*n stones are arranged in an m*n matrix A. Two players play a game: they choose a stone in the matrix, say the stone in position A(i, j), then this stone together with all the stones to the northeast of it are removed (i.e., stones in the submatrix [A1j:Ain] are removed). Two players take turns to choose and remove the stones. Whoever removes the last stone (or stones) loses the game.

Prove: There's a strategy for the first player to win.

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I can show that when m=n, the first player has a winning strategy. But I don't know how show the same result for m<n.