Double Tower of Hanoi: In this variation of the Tower of Hanoi there are three poles in

Chapter 5, Problem 21

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Double Tower of Hanoi: In this variation of the Tower of Hanoi there are three poles in a row and 2n disks, two of each of n different sizes, where n is any positive integer. Initially one of the poles contains all the disks placed on top of each other in pairs of decreasing size. Disks are transferred one by one from one pole to another, but at no time may a larger disk be placed on top of a smaller disk. However, a disk may be placed on top of one of the same size. Let \(t_{n}\) be the minimum number of moves needed to transfer a tower of 2n disks from one pole to another.

a. Find \(t_{1} and t_{2}\).

b. Find \(t_{3}\).

c. Find a recurrence relation for \(t_{1}, t_{2}, t_{3}\), . . . .

Text Transcription:

t_n

t_1 and t_2

t_3

t_1, t_2, t_3