Sprague-Grundy Values of the R-Wythoff Game
نویسنده
چکیده
We examine the Sprague-Grundy values of the game of R-Wythoff, a restriction of Wythoff’s game introduced by Ho, where each move is either to remove a positive number of tokens from the larger pile or to remove the same number of tokens from both piles. Ho showed that the P -positions of R-Wythoff agree with those of Wythoff’s game, and found all positions of Sprague-Grundy value 1. We describe all the positions of Sprague-Grundy value 2 and 3, and also conjecture a general form of the positions of Sprague-Grundy value g.
منابع مشابه
On the Sprague-Grundy Values of the 𝔽-Wythoff Game
We examine the Sprague-Grundy values of F-Wythoff, a restriction of Wythoff’s game introduced by Ho, where the integer ratio of the pile sizes must be preserved if the same number of tokens is removed from both piles. We answer two conjectures raised by Ho. First, we show that each column of Sprague-Grundy values is ultimately additively periodic. Second, we prove that every diagonal of Sprague...
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