<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</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%">Science of Computer Programming</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2013</style></year></dates><urls><related-urls><url><style face="normal" font="default" size="100%">https://haslab.uminho.pt/sites/default/files/jff/files/2013-algorithmicsolitairegamesextended.pdf</style></url></related-urls></urls><volume><style face="normal" font="default" size="100%">78</style></volume><pages><style face="normal" font="default" size="100%">2029-2046</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">11</style></issue></record></records></xml>