Suppose that you have
several numbered billiard balls on a pool table. The smallest
possible number on the ball is “1”. At each step, you remove a
billiard ball from the table. If the ball removed is numbered
n, you replace it with n balls randomly numbered
less than n. For example, if you remove
the “5” ball, you replace it with balls numbered “2”, “1”, “1”,
“4”, and “3”, where numbers 2, 1, 1, 4, and 3 were randomly...