Alvin

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Alice and Bob play a game using a 10 x 10 chocolate bar. They take turns, with Alice going first. A move consists of choosing any existing cell (i, j) of the grid, and eating that cell along with all cells (r, c) such that r >= i and c >= j. The player who eats the last remaining piece (the cell at (1, 1)) loses the game. Who has the winning strategy?