The Algorithmics of Solitaire-Like Games (Extended Version)

Abstract

One-person solitaire-like games are explored with a view to using them in teaching algo- rithmic problem solving. The key to understanding solutions to such games is the iden- tification 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 poly- nomials 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.

Publication
In Science of Computer Programming 78 (2013), pp. 2029-2046
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João F. Ferreira
Computer Scientist

My research interests include software reliability, software verification, and formal methods applied to software engineering. I am also interested in interactive storytelling. For more details, see some of my projects or my selected (or recent) publications. More posts are available in my blog. Follow me on Twitter or add me on LinkedIn.