# 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.