The algorithmics of solitaire-like games

Backhouse, Roland; Chen, Wei; Ferreira, Jo�o F.

Abstract

One-person solitaire-like games are explored with a view to using them in teaching algorithmic problem solving. The key to understanding solutions to such games is the identification of invariant properties of polynomial arithmetic. We demonstrate this via three case studies: solitaire itself, tiling problems and a novel class of 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, which we call ``replacement-set 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 present an algorithm to solve arbitrary instances of replacement-set games and we show various ways of constructing infinite (solvable) classes of replacement-set games.

Citation

Backhouse, R., Chen, W., & Ferreira, J. F. (2013). The algorithmics of solitaire-like games. Science of Computer Programming, 78(11), 2029-2046. https://doi.org/10.1016/j.scico.2012.07.007

• Journal Article Type: Article
• Acceptance Date: Aug 10, 2011
• Online Publication Date: Jul 27, 2012
• Publication Date: 2013-11
• Deposit Date: Jan 7, 2013
• Publicly Available Date: Jan 7, 2013
• Journal: Science of Computer Programming
• Print ISSN: 0167-6423
• Electronic ISSN: 1872-7964
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 78
• Issue: 11
• Pages: 2029-2046
• DOI: https://doi.org/10.1016/j.scico.2012.07.007
• Keywords: Software
• Public URL: https://nottingham-repository.worktribe.com/output/1007019
• Publisher URL: http://dx.doi.org/10.1016/j.scico.2012.07.007