Sprague-Grundy Values of the $\mathcal{R}$-Wythoff Game
نویسندگان
چکیده
منابع مشابه
Sprague-Grundy Values of the R-Wythoff Game
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...
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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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We present two new results on Wythoff’s Grundy function G. The first one is a proof that for every integer g 0, the g-values of G are within a bounded distance to their corresponding 0-values. Since the 0-values are located roughly along two diagonals, of slopes and , the g-values are contained within two strips of bounded width around those diagonals. This is a generalization of a previous res...
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The game Euclid, introduced and named by Cole and Davie, is played with a pair of nonnegative integers. The two players move alternatively, each subtracting a positive integer multiple of one of the integers from the other integer without making the result negative. The player who reduces one of the integers to zero wins. Unfortunately, the name Euclid has also been used for a subtle variation ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2015
ISSN: 1077-8926
DOI: 10.37236/4579