| Discussion: | Traffic Jam Applet tool |
| Topic: | mathmatical induction |
| Related Item: | http://mathforum.org/mathtools/tool/10/ |
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| Subject: | mathmatical induction |
| Author: | booya |
| Date: | Mar 11 2004 |
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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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