Problem 61 Solution

Think of the problem as a random walk where the probability is p of moving to the left and 1-p of moving to the right. The expected change in the position on the number line per move is p*(+1) + (1-p)*(-1) = 2p-1. The first flip resulted in moving one space to the right. The expected number of moves to move one space to the left is the inverse of the expected movement, which equals 1/(2p-1).

It may not seem reasonable to take the last step on faith but millions of computer trials have verified the answer.

Michael Shackleford, A.S.A.