The Towers of Hanoi Puzzle
The description of this problem is taken from the book by Douglas Baldwin and Greg W Scragg (2004), Algorithms and Data Structures: The Science of Computing. Hingham MA: Charles River Media. Legend tells of an ageless temple in the city of Hanoi. Within this temple are three poles of diamond piercing 64 golden disks of varying sizes. At the moment of creation, the disks were stacked smaller-on-top-of-larger on the leftmost pole. Since then, the monks of the temple have been moving the disks from the left pole to the right pole, subject to the following rules:- The monks only move one disk at a time.
- Every disk taken off a pole has to be put back on some pole before moving another disk.
- The monks never put a disk on top of a smaller one.
When all the disks have been moved to the right-hand pole, the purpose of creation will have been fulfilled and the universe will end. It’s not immediately obvious how (or even if) the monks can move the disks to the right-hand pole while obeying all the rules. The Towers of Hanoi puzzle amounts to figuring out a way. It isn’t essential to the puzzle that there are 64 disks, and in fact, a 64-disk tower would be quite unwieldy. Thus, the problem is usually posed without reference to the specific number of disks, as follows:
Given n disks stacked smaller-on-larger on the left-most of three poles, move all the disks to the right-most pole, subject to the rules given above.
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