Towers of Hanoi

The first picture below is the starting position of the infamous Towers of Hanoi puzzle. It is played with three pegs and a set of disks (with holes in the middle) all of different sizes. In the starting position, the disks are all placed on the leftmost peg, from the smallest at the top to the largest at the bottom. The puzzle can have any number of disks; for simplicity, we will assume we are working with five disks.

The object of this classic puzzle is to transfer all the disks from the first peg to one of the other two pegs. Disks may only be moved one at a time, and no disk may ever be placed on top of a smaller disk. The second picture below depicts one of the many possible legal positions.

The Towers of Hanoi is an interesting puzzle, but for this month's Problem of the Month, I have a different goal in mind. These two pictures show two different legal ways to arrange the five disks. How many such arrangements are there? Remember, no disk may be placed on top of a smaller disk.

Send your answers to this problem to me (Joseph DiMuro) at joseph.dimuro@biola.edu by May 31, 2013.