Article ID Journal Published Year Pages File Type
421244 Discrete Applied Mathematics 2011 8 Pages PDF
Abstract

Berlekamp asked the question “What is the habitat of ∗2∗2?” (See Guy, 1996 [6].) It is possible to generalize the question and ask “For a game GG, what is the largest nn such that ∗n∗n is a position of GG?” This leads to the concept of the nim dimension. In Santos and Silva (2008) [8] a fractal process was proposed for analyzing the previous questions. For the same purpose, in Santos and Silva (2008) [9], an algebraic process was proposed. In this paper we implement a third idea related to embedding processes. With Alan Parr’s traffic lights, we exemplify the idea of estimating the “difficulty” of the game and proving that its nim dimension is infinite.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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