<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>5</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Roland Backhouse</style></author><author><style face="normal" font="default" size="100%">Wei Chen</style></author><author><style face="normal" font="default" size="100%">João F. Ferreira</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The Algorithmics of Solitaire-Like Games</style></title><secondary-title><style face="normal" font="default" size="100%">Mathematics of Program Construction (LNCS 6120)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2010</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;br /&gt;
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.&lt;/p&gt;
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