Concept explainers
Tower of Hanoi The result in Exercise 39 suggest that the minimum number of moves required to transfer n disks from one peg to another is given by the formula
a) Verify the formula for
b) Write the induction hypothesis.
c) How many moves are needed to transfer all but the largest of
d) How many moves are needed to transfer the largest disk to an empty peg?
e) How many moves are needed to transfer the first k disks back onto the largest one?
f) How many moves are needed to accomplish steps c, d, and e?
g) Show that part f can be written in the form
h) Write the conclusion of the proof.
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