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Tower of Hanoi

Tower of Hanoi is a complex tape backup strategy that's useful for archiving data for an extended period of time in an economical manner. The strategy, which is based on a mathematical puzzle invented by the French mathematician Edouard Lucas, uses a cycle of exponential retention periods instead of a large number of tapes.

Lucas, who is well-known for his study of the Fibonacci sequence and his work with prime numbers, loved recreational mathematics. His Tower of Hanoi puzzle, which is still marketed as a toy for children, has a platform with three poles. There is a stack of disks or rings on the first pole. The stack looks like a pyramid; each disk going down the pole is a little larger than the one above it. To solve Lucas' puzzle, the player must move all the discs from the first pole to the third pole in the fewest possible moves. There are two rules: only one disk can be moved at a time and a larger disc cannot be placed on top of a smaller one.

There are several ways to solve the puzzle, but one of the easiest ways is to start with only one ring -- and then figure out how to solve it with two rings -- and then figure out how to solve it with three rings. Once you have solved the puzzle using small numbers, patterns will begin to emerge. This is known as a recursive solution. (See recursion.) A recursive pattern uses the information gained from one step to figure out the next step.


Number of disks
Fewest number of moves
1
1
2
3
3
7
4
15
5
31

Like the puzzle, Towers of Hanoi backup uses a recursive pattern for scheduling tapes. It enables an administrator to restore data from backups that are one, two, four, eight and sixteen days old, yet only use five tapes. This strategy, which requires backup software to support the complex rotation schedule, is good for small businesses that need to be able to do full restores.

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