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2014 The sock matching problem
Sarah Gilliand, Charles Johnson, Sam Rush, Deborah Wood
Involve 7(5): 691-697 (2014). DOI: 10.2140/involve.2014.7.691

Abstract

When matching socks after doing the laundry, how many unmatched socks can appear in the process of drawing one sock at a time from the basket? By connecting the problem of sock matching to the Catalan numbers, we give the probability that k unmatched socks appear. We also show that, for each fixed k, this probability approaches 1 as the number of socks becomes large enough. The relation between the number of socks and the k for which a given probability is first reached is also discussed, but a complete answer is open.

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Sarah Gilliand. Charles Johnson. Sam Rush. Deborah Wood. "The sock matching problem." Involve 7 (5) 691 - 697, 2014. https://doi.org/10.2140/involve.2014.7.691

Information

Received: 21 August 2013; Accepted: 25 November 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1297.05019
MathSciNet: MR3245844
Digital Object Identifier: 10.2140/involve.2014.7.691

Subjects:
Primary: 05A15 , 05A16
Secondary: 00A69 , 03B48

Keywords: Catalan numbers , Dyck paths , sock matching

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 5 • 2014
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