Doing some laundry last night, I threw a duvet cover and nine pairs of socks into the dryer together. (Household hint: Don’t.) The duvet cover is a giant fabric pouch with a slit along one side; think of a queen-size pita pocket. Initially, all the socks were outside the pouch. When I pulled the load out of the dryer, all but three of the socks were inside the cover.
There’s nothing obvious about the geometry of this big, floppy bag that would suggest it has any special ability to capture socks. It’s not shaped like a fish trap with a funnel opening. In the random tumbling of the dryer, I would have thought that socks would move into or out of the opening with the same probability. But if that’s the case, then finding a 15–3 distribution is quite a fluke. There are 218 = 262,144 ways of arranging the socks in two groups, and only 5,220 of them have three or fewer socks in one of the groups. That’s less than 2 percent and a little beyond the 2σ level of unlikelihood. Does Maxwell’s sock demon live in my dryer?