A Generalization of Wythoff's Game*

Abstract

W.A. Wythoff [1] in 1907 defined a modification of the game of Nim by the following rules:(i)there are two players who play alternately;(ii)initially there are two piles of matches, an arbitrary number in each pile;(iii)a player may take an arbitrary number of matches from one pile or an equal number from both piles but he must take at least one match;(iv)the player who takes the last match wins the game.If, after his move, a player leaves one match in one pile and two in the other he can force a win; for if his opponent takes one match from the pile containing two he can take both remaining matches; and similarly for the other possibilities.