Frustration solitaire

Peter G. Doyle; Charles M. Grinstead; J. Laurie Snell

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Frustration solitaire

Peter G. Doyle·Charles M. Grinstead·J. Laurie Snell

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Abstract

In this expository article, we discuss the rank-derangement problem, which asks for the number of permutations of a deck of cards such that each card is replaced by a card of a different rank. This combinatorial problem arises in computing the probability of winning the game of `frustration solitaire'. The solution is a prime example of the method of inclusion and exclusion. We also discuss and announce the solution to Montmort's `Probleme du Treize', a related problem dating back to circa 1708.

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Peter G. Doyle, Charles M. Grinstead, J. Laurie Snell. 2009-04-02. Frustration solitaire. https://arxiv.org/abs/math/0703900

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