### Abstract

Original language | English |
---|---|

Pages (from-to) | 217–231 |

Number of pages | 15 |

Journal | American Mathematical Monthly |

Volume | 114 |

Issue number | 3 |

Publication status | Published - Mar 2007 |

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### Keywords

- mathematical puzzles
- mathematicians

### Cite this

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*American Mathematical Monthly*, vol. 114, no. 3, pp. 217–231.

**Conway's napkin problem.** / Claesson, Anders.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Conway's napkin problem

AU - Claesson, Anders

PY - 2007/3

Y1 - 2007/3

N2 - The napkin problem was first posed by John H. Conway, and written up as a 'toughie' in Mathematical Puzzles: A Connoisseur's Collection, by Peter Winkler. To paraphrase Winkler's book, there is a banquet dinner to be served at a mathematics conference. At a particular table, n men are to be seated around a circular table. There are n napkins, exactly one between each of the place settings. Being doubly cursed as both men and mathematicians, they are all assumed to be ignorant of table etiquette. The men come to sit at the table one at a time and in random order. When a guest sits down, he will prefer the left napkin with probability p and the right napkin with probability q = 1 - p. If there are napkins on both sides of the place setting, he will choose the napkin he prefers. If he finds only one napkin available, he will take that napkin (though it may not be the napkin he wants). The third possibility is that no napkin is available, and the unfortunate guest is faced with the prospect of going through dinner without any napkin! Using a combinatorial approach, we answer questions like: What is the probability that every guest receives a napkin? How many guests do we expect to be without a napkin? How many guests are happy with the napkin they receive?

AB - The napkin problem was first posed by John H. Conway, and written up as a 'toughie' in Mathematical Puzzles: A Connoisseur's Collection, by Peter Winkler. To paraphrase Winkler's book, there is a banquet dinner to be served at a mathematics conference. At a particular table, n men are to be seated around a circular table. There are n napkins, exactly one between each of the place settings. Being doubly cursed as both men and mathematicians, they are all assumed to be ignorant of table etiquette. The men come to sit at the table one at a time and in random order. When a guest sits down, he will prefer the left napkin with probability p and the right napkin with probability q = 1 - p. If there are napkins on both sides of the place setting, he will choose the napkin he prefers. If he finds only one napkin available, he will take that napkin (though it may not be the napkin he wants). The third possibility is that no napkin is available, and the unfortunate guest is faced with the prospect of going through dinner without any napkin! Using a combinatorial approach, we answer questions like: What is the probability that every guest receives a napkin? How many guests do we expect to be without a napkin? How many guests are happy with the napkin they receive?

KW - mathematical puzzles

KW - mathematicians

UR - http://www.jstor.org/stable/27642167

M3 - Article

VL - 114

SP - 217

EP - 231

JO - American Mathematical Monthly

JF - American Mathematical Monthly

SN - 0002-9890

IS - 3

ER -