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Wythoff's game is a two-player mathematical subtraction game, played with two piles of counters. Players take turns removing counters from one or both piles; when removing counters from both piles, the numbers of counters removed from each pile must be equal. The game ends when one player removes the last counter or counters, thus winning.
An equivalent description of the game is that a single chess queen is placed somewhere on a large grid of squares, and each player can move the queen towards the lower left corner of the grid: south, west, or southwest, any number of steps. The winner is the player who moves the queen into the corner. The two Cartesian coordinates of the queen correspond to the sizes of two piles in the formulation of the game involving removing counters from piles.
Martin Gardner in his March 1977 "Mathematical Games column" in Scientific American claims that the game was played in China under the name 捡石子 jiǎn shízǐ ("picking stones").[1] The Dutch mathematician W. A. Wythoff published a mathematical analysis of the game in 1907.[2]
- ^ Wythoff's game at Cut-the-knot, quoting Martin Gardner's book Penrose Tiles to Trapdoor Ciphers
- ^ Wythoff, W. A. (1907), "A modification of the game of nim", Nieuw Archief voor Wiskunde, 7 (2): 199–202