1. Find the shortest sequence of moves that transfers a tower of n disks from the left peg A to the right peg B, if direct moves between A and B are disallowed. (Each move must be to or from the middle peg. As usual, a larger disk must never appear above a smaller one.) 2. Show that, in the process of transferring a tower under the restrictions of the preceding exercise, we will actually encounter every properly stacked arrangement of n disks on three pegs 3. Are there any starting and ending configurations of n disks on three pegs that are more than 2^n - 1 move apart, under Lucas's original rules? (these three questions are related) Thank you