Consider two urns, A and B, where initially A contains a large number n of balls and B is empty. At each step, with equal probability, either we pick a ball at random in A and place it in B, or vice-versa (provided of course that A, or B, is not empty). The number of balls in B after n steps is of order n√, and this number remains essentially the same after n√ further steps. Observe that each b...