Frustration solitaire

• Published in 2007
• Added on 2017-08-10

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.

Links

• http://arxiv.org/abs/math/0703900v2
• http://arxiv.org/pdf/math/0703900v2

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}
}