# Frustration solitaire

• Published in 2007
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.

### 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}
}