Impact of binary and Fibonacci expansions of numbers on winning strategies for Nim-like games |
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| Authors: | Takemasa Ooya Jin Akiyama |
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| Institution: | 1. Department of Mathematical Sciences Tokai University Kitakaname Hiratsuka Japan 259-1207 ooya@ss.u-tokai.ac.jp;2. Research Institute of Educational Development Tokai University Tomigaya Shibuya Tokyo Japan 151-0063 fwjb5117@mb.infoweb.ne.jp |
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| Abstract: | An analysis of the successful moves for the game of solitaire, played in reverse, has resulted in the formulation of a set of rules, the observance of which leads to success. The principal rules entail symmetry properties and also the density of packing of pegs. Subsidiary rules are formulated in terms of both the current location of play and its direction. When play has proceeded for some way, a difficulty is encountered which can be surmounted by applying a modified form of the rule for density of packing. The interesting fact emerges that within the game of solitaire there are two separate symmetrical situations which are species of mini‐solitaire. |
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