Reformed Permutations in Mousetrap and Its Generalizations
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Alberto Maria Bersani
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.
© de Gruyter 2010
Articles in the same Issue
- Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
- On the Iteration of a Function Related to Euler's φ-Function
- An Explicit Evaluation of the Gosper Sum
- On the Frobenius Problem for {ak, ak + 1, ak + a, . . . , ak + ak−1}
- Generalizing the Combinatorics of Binomial Coefficients via -Nomials
- Finding Almost Squares V
- On Relatively Prime Subsets and Supersets
- Reformed Permutations in Mousetrap and Its Generalizations
- On Ternary Inclusion-Exclusion Polynomials
- Sums and Products of Distinct Sets and Distinct Elements in ℂ
Articles in the same Issue
- Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem
- On the Iteration of a Function Related to Euler's φ-Function
- An Explicit Evaluation of the Gosper Sum
- On the Frobenius Problem for {ak, ak + 1, ak + a, . . . , ak + ak−1}
- Generalizing the Combinatorics of Binomial Coefficients via -Nomials
- Finding Almost Squares V
- On Relatively Prime Subsets and Supersets
- Reformed Permutations in Mousetrap and Its Generalizations
- On Ternary Inclusion-Exclusion Polynomials
- Sums and Products of Distinct Sets and Distinct Elements in ℂ
