# Frustration solitaire

- Published in 2007
- Added on

In the collections

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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### BibTeX entry

@article{Frustrationsolitaire, title = {Frustration solitaire}, 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.}, url = {http://arxiv.org/abs/math/0703900v2 http://arxiv.org/pdf/math/0703900v2}, author = {Peter G. Doyle and Charles M. Grinstead and J. Laurie Snell}, comment = {}, urldate = {2017-08-10}, archivePrefix = {arXiv}, eprint = {math/0703900}, primaryClass = {math.PR}, year = 2007, collections = {easily-explained,games-to-play-with-friends,probability-and-statistics,puzzles} }