Mathematical Citation Quotient (MCQ) 2016: 0.40
2-Pile Nim with a Restricted Number of Move-Size Imitations
We study a variation of the combinatorial game of 2-pile Nim. Move as in 2-pile Nim but with the following constraint: Suppose the previous player has just removed say x > 0 tokens from the shorter pile (either pile in case they have the same height). If the next player now removes x tokens from the larger pile, then he imitates his opponent. For a predetermined natural number p, by the rules of the game, neither player is allowed to imitate his opponent on more than p – 1 consecutive moves. We prove that the strategy of this game resembles closely that of a variant of Wythoff Nim—a variant with a blocking manoeuvre on p – 1 diagonal positions. In fact, we show a slightly more general result in which we have relaxed the notion of what an imitation is. The paper includes an appendix by Peter Hegarty, Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, .
Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.