Solved: Tower of Hanoi Poles in a Circle: Suppose that
Chapter 5, Problem 5.223(choose chapter or problem)
Tower of Hanoi Poles in a Circle: Suppose that instead of being lined up in a row, the three poles for the original Tower of Hanoi are placed in a circle. The monks move thedisksonebyonefromonepoletoanother,buttheymay onlymovedisksoneoverinaclockwisedirectionandthey may never move a larger disk on top of a smaller one. Let cn be the minimum number of moves needed to transfer a pile of n disks from one pole to the next adjacent pole in the clockwise direction. a. Justify the inequality ck 4ck1 +1 for all integers k 2.b. The expression 4ck1 +1 is not the minimum number of moves needed to transfer a pile of k disks from one pole to another. Explain, for example, why c3=4c2 +1.
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