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 unmatched socks appear. We also show that, for each fixed , this probability approaches as the number of socks becomes large enough. The relation between the number of socks and the for which a given probability is first reached is also discussed, but a complete answer is open.
"The sock matching problem." Involve 7 (5) 691 - 697, 2014. https://doi.org/10.2140/involve.2014.7.691