Book
The Algorithmics of Solitaire-Like Games.
| Title: | The Algorithmics of Solitaire-Like Games. |
|---|---|
| Authors: | Backhouse, Roland, Chen, Wei, Ferreira, João F. |
| Source: | Mathematics of Program Construction (9783642133206); 2010, p1-18, 18p |
| 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. [ABSTRACT FROM AUTHOR] |
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| DOI: | 10.1007/978-3-642-13321-3_1 |
| Database: | Complementary Index |
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