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Discussion: Roundtable
Topic: mathmatical induction


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Subject:   mathmatical induction
Author: booya
Date: Mar 11 2004
I am having a terrible time trying to figure this problem out, please help:

There are three pegs on a board.  On one peg are "n disks", each smaller than
the one on which it rests.  The problem is to move this pile of disks to another
peg.  The final order must be the same, but you can move only 1 disk at a time
and can never place a larger disk on a smaller one.

a.  What is the smallest number of moves needed to move: 1 disk? 2 disks? 3
disks? 4 disks?
b.  Conjecture a formula for the smallest number of moves needed to move n
disks.
c.  Prove this formula by mathematical induction.

I cannot even get anywhere near as to how to start.  Thanks.

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