Reformed permutations in Mousetrap and its generalizations
نویسنده
چکیده
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 simulations. Furthermore, we introduce a new 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 new 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.
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