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The Freshman's Approach to Conway's Napkin Problem
Department of Mathematical Sciences, University of Gothenburg, Chalmers University of Technology, Gothenburg.ORCID iD: 0000-0002-6444-7878
2008 (English)In: The American mathematical monthly, ISSN 0002-9890, E-ISSN 1930-0972, Vol. 115, no 6, p. 492-498Article in journal (Refereed) Published
Abstract [en]

In the March 2006 issue of the MONTHLY, Claesson and Petersen gave a thorough solution to Conway's napkin problem. The problem is the following: Assume that n mathematicians arrive in random order at a conference dinner with a circular table, and that the napkins are placed exactly halfway between the plates so that the guests do not know whether they are supposed to use the right or the left napkin. Each guest prefers these napkins with probabilities p and 1-p, respectively, and tries her preferred alternative before trying the other, if the preferred napkin has been taken. Which proportion of guests is expected to sit down at a place where both adjacent napkins have been taken and thus be without a napkin? Claesson and Petersen use a system of generating functions to compute both the expectation and the variance of this proportion and to address similar questions, for instance regarding the number of guests who get a napkin though not the preferred one. However, these expectations can also be computed using purely elementary methods, such as the binomial theorem. We present the freshman's approach to the napkin problem and related problems, for instance the one with French diners mentioned, but not solved, by Claesson and Petersen.

Place, publisher, year, edition, pages
Washington, USA: Mathematical Association of America , 2008. Vol. 115, no 6, p. 492-498
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-41705ISI: 000256506200002Scopus ID: 2-s2.0-46449123123OAI: oai:DiVA.org:oru-41705DiVA, id: diva2:780963
Available from: 2015-01-15 Created: 2015-01-15 Last updated: 2017-12-05Bibliographically approved

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