# Deranged Socks

by Sally Cockburn and Joshua Lesperance

Year of Award: 2014

Award: Allendoerfer

Publication Information: Mathematics Magazine, vol. 86, 2013, pp. 97-109.

Summary (adapted from the MAA Prizes and Awards booklet for MathFest 2014): How many ways can $n$ people each choose two gloves from a pile of $n$ distinct pairs of gloves, so that nobody gets a matching pair? In this article, authors Sally Cockburn and Joshua Lesperance consider a challenging twist on this familiar combinatorics problem, replacing gloves with socks. They ask, “How many ways can $n$ people each choose two socks from a pile of $n$ distinct pairs of socks, with no one getting a matching pair?”. The sock problem extends the glove problem by removing the crucial assumption that right- and left-handed gloves are distinguishable.

About the Authors: (From the MathFest 2014 MAA Prizes and Awards Booklet)

Sally Cockburn was born and raised in Ottawa, Canada. She first fell in love with mathematics at Queen’s University, where she completed a Bachelor of Science in 1982 and a Master’s of Science in 1984. While at Yale University pursuing a Ph. D., her research in algebraic topology took an unexpected detour into generating functions and combinatorial identities, and she became hooked on discrete mathematics. Since joining the Mathematics Department at Hamilton College in 1991, her teaching and research specialization has been in combinatorics, graph theory and linear optimization, although she also likes to dabble in the philosophy of mathematics. Sally is an avid squash player and helped coach Hamilton's varsity squash teams for ten years. Whenever possible, she escapes to go hiking, biking, kayaking and skiing in the wilds of the Adirondacks.

Joshua Lesperance has a B.S. in applied mathematics from Rochester Institute of Technology and both a M.S. and a Ph.D. from the University of Notre Dame, where he studied algebraic geometry. He has taught mathematics at Hamilton, Oberlin, Skidmore, and Franklin & Marshall colleges. Since leaving Notre Dame, his research interests have shifted back towards his applied mathematics roots, most recently working on applications of spherical harmonics in the understanding of human perception of 3-dimensional shape. Joshua currently lives in Columbus, Ohio with his wife Karilyn and their two Siberian Huskies, Mia and Kai.

Subject classification(s): Discrete Mathematics | Combinatorics
Publication Date:
Monday, August 11, 2014