Four-Pole Tower of Hanoi: Suppose that the Tower of Hanoi
Chapter 5, Problem 19E(choose chapter or problem)
Problem 19E
Four-Pole Tower of Hanoi: Suppose that the Tower of Hanoi problem has four poles in a row instead of three. Disks can be transferred one by one from one pole to any other pole, but at no time may a larger disk be placed on top of a smaller disk. Let sn be the minimum number of moves needed to transfer the entire tower of n disks from the left-most to the right-most pole.
a. Find s1, s2, and s3.
b. Find s4.
c. Show that sk ≤ 2sk–2 + 3 for all integers k ≥ 3.
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