# 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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## Other information

- key
- Frustrationsolitaire
- type
- article
- date_added
- 2017-08-10
- date_published
- 2007-07-11

### BibTeX entry

@article{Frustrationsolitaire, key = {Frustrationsolitaire}, type = {article}, title = {Frustration solitaire}, author = {Peter G. Doyle and Charles M. Grinstead and J. Laurie Snell}, 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.}, comment = {}, date_added = {2017-08-10}, date_published = {2007-07-11}, urls = {http://arxiv.org/abs/math/0703900v2,http://arxiv.org/pdf/math/0703900v2}, collections = {Easily explained,Games to play with friends,Probability and statistics,Puzzles}, url = {http://arxiv.org/abs/math/0703900v2 http://arxiv.org/pdf/math/0703900v2}, urldate = {2017-08-10}, archivePrefix = {arXiv}, eprint = {math/0703900}, primaryClass = {math.PR}, year = 2007 }