Discussion:  Roundtable 
Topic:  mathmatical induction 
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Subject:  RE: mathmatical induction 
Author:  Michael McKelvey 
Date:  Mar 11 2004 
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 reappearing 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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