We study a card game called Mousetrap, together with its generalization He Loves Me, He Loves Me Not. We first present some results for the latter game, based, on one hand, on theoretical considerations and, on the other one, on Monte Carlo trials. Furthermore, we introduce a combinatorial algorithm, which allows us to obtain the best result at least for French card decks (52 cards with 4 suits). We then apply the algorithm to the study of Mousetrap and Modular Mousetrap, improving recent results. Finally, by means of our algorithm, we study the reformed permutations in Mousetrap, Modular Mousetrap and He Loves Me, He Loves Me Not, attaining new results which give some answers to several questions posed by Cayley and by Guy and Nowakowski in their papers.

Reformed permutations in Mousetrap and its generalizations / Bersani, Alberto Maria. - In: INTEGERS. - ISSN 1553-1732. - ELETTRONICO. - 10:5(2010), pp. 575-622. [10.1515/integ.2010.101]

Reformed permutations in Mousetrap and its generalizations

BERSANI, Alberto Maria
2010

Abstract

We study a card game called Mousetrap, together with its generalization He Loves Me, He Loves Me Not. We first present some results for the latter game, based, on one hand, on theoretical considerations and, on the other one, on Monte Carlo trials. Furthermore, we introduce a combinatorial algorithm, which allows us to obtain the best result at least for French card decks (52 cards with 4 suits). We then apply the algorithm to the study of Mousetrap and Modular Mousetrap, improving recent results. Finally, by means of our algorithm, we study the reformed permutations in Mousetrap, Modular Mousetrap and He Loves Me, He Loves Me Not, attaining new results which give some answers to several questions posed by Cayley and by Guy and Nowakowski in their papers.
2010
combina- torial game theory; combinatorial analysis; computational combinatorics; derangements; deterministic solitaires; discrete dynamical systems; monte carlo simulations; mousetrap; reformed permutations
01 Pubblicazione su rivista::01a Articolo in rivista
Reformed permutations in Mousetrap and its generalizations / Bersani, Alberto Maria. - In: INTEGERS. - ISSN 1553-1732. - ELETTRONICO. - 10:5(2010), pp. 575-622. [10.1515/integ.2010.101]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/67798
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