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The Algorithmics of Solitaire-Like Games

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Mathematics of Program Construction (MPC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6120))

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Abstract

Puzzles and games have been used for centuries to nurture problem-solving skills. Although often presented as isolated brain-teasers, the desire to know how to win makes games ideal examples for teaching algorithmic problem solving. With this in mind, this paper explores one-person solitaire-like games.

The key to understanding solutions to solitaire-like games is the identification of invariant properties of polynomial arithmetic. We demonstrate this via three case studies: solitaire itself, tiling problems and a collection of novel one-person games. The known classification of states of the game of (peg) solitaire into 16 equivalence classes is used to introduce the relevance of polynomial arithmetic. Then we give a novel algebraic formulation of the solution to a class of tiling problems. Finally, we introduce an infinite class of challenging one-person games inspired by earlier work by Chen and Backhouse on the relation between cyclotomic polynomials and generalisations of the seven-trees-in-one type isomorphism. We show how to derive algorithms to solve these games.

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Backhouse, R., Chen, W., Ferreira, J.F. (2010). The Algorithmics of Solitaire-Like Games. In: Bolduc, C., Desharnais, J., Ktari, B. (eds) Mathematics of Program Construction. MPC 2010. Lecture Notes in Computer Science, vol 6120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13321-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-13321-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13320-6

  • Online ISBN: 978-3-642-13321-3

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