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In the Tower of Hanoi puzzle, suppose our goal is to transfer all n disks from peg 1 to peg 3, but we cannot move a disk directly between pegs 1 and 3. Each move of a disk must be a move involving peg 2. As usual, we cannot place a disk on top of a smaller disk.
a) Find a recurrence relation for the number of moves required to solve the puzzle for n disks with this added restriction.
b) Solve this recurrence relation to find a formula for the number of moves required to solve the puzzle for n disks.
c) How many different arrangements are there of the n disks on three pegs so that no disk is on top of a smaller disk?
d) Show that every allowable arrangement of the n disks occurs in the solution of this variation of the puzzle.
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Chapter 8 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
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