Problem: Shoe laces

Cosmin Negruseri
28 aprilie 2016

Here's a probability puzzle I've learned from Alex Ku:

There are N shoe laces in a bag. A move consists of randomly picking two shoe lace ends from the bag, tying them together and then placing them back in the bag. We keep going until we can't find any shoe lace ends to tie. What is the expected number of different shoe lace cycles we'll have at the end.

P.S. Please don't spoil the problem if you've seen it before.