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Discussion: Traffic Jam Applet tool
Topic: mathmatical induction
Related Item: http://mathforum.org/mathtools/tool/10/


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Subject:   RE: mathmatical induction
Author: Michael McKelvey
Date: Mar 11 2004
Ah yes, the good old Towers of Hanoi problem!

Well, since I can't do your homework for you, I won't *give* you the answers.
However, I can try to get you started...

a) You should be able to figure out at least the first couple without any
help...  Start looking for patterns.  What are some general sequences of moves
you find yourself doing a lot?  Do you see any sequences of moves that occurred
for smaller numbers of disks re-appearing when you try the puzzle with more
disks?

b) Play with this tool:
http://mathforum.org/mathtools/tool.html?&id=407
It may help you in trying to find the minimum # of moves

c) Start with your assumed formula f(x).
There are 2 steps to mathematical induction:
 1) Prove that this formula works for f(1) --> this should be trivial; just
solve for f(1)
 2) Prove that IF YOUR FORMULA WORKS FOR f(n), then it works for f(n+1). In
other words, *assume* that f(n) works, and try to show the following:

M = <some term you've figured out involving n>
f(n) + M = f(n+1)

I know that's a vague explanation, but hopefully it helps.  If you need help
with Mathematical induction, there are a lot of places online that you can go.
Try Googling "mathematical induction".  It'll give you plenty of results.

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