There's a pile of socks freshly washed and dried. Call it 2n of them (all pairs).
You pull one out at random. You don't have a pair (obvs) so you lay it out in the holding area. Holding area has 1 sock.
You pull another random sock from the pile. It doesn't match any of the socks in your holding area, so you lay it down next to the first. Holding area has 2 socks.
You pull out a 3rd sock. It matches one in the holding area. So you roll them both up and put them in the drawer. Holding area now has 1 sock.
What's the expected maximum number of socks in the holding area?
Or, what's a reasonable space (measured in socks) for the holding area?
