Abstract:We examine the Sprague-Grundy values of the game of $\mathcal{R}$-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 $\mathcal{R}$-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 … Show more
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