Problem of the Week

Because of the upcoming Spring Break, this week's puzzle will remain open for two weeks. Enjoy your break!!  Happy St. Patrick's Day.

You may be familiar with the puzzle known as the Towers of Hanoi.  There are three posts and n disks of distinct radii each with a hole in the middle.  At the start the disks are stacked at one of the posts in order of descending size, with the disk of smallest radius on top.  The problem is to transfer the disks from one post to another by moving one disk at a time from one post onto another one and never stacking a larger disk on a smaller one.

(If you have never seen this puzzle show first that the number of moves required for this task is 2ⁿ-1.)

In this week's puzzle I ask you to look at the Tower puzzle with four posts.

What is the fewest number of moves required to transfer eight disks from one post to another if you have four posts to work with?

For those who can't get enough: Figure out good upper and lower bounds on the number of steps required to solve the general Tower puzzle with four posts.

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ã2002 Alberto L. Delgado