Initially three disks of different sizes, each having a hole in its center, are placed as shown in the diagram below, all of them about one of three pegs. It is desired to transfer their initial configuration to the third peg, moving them one at a time in such a way that only the top disk on a peg is ever the disk being moved and a larger disk is never placed on top of a smaller disk. How can this be done?

First solve the problems that are given. Next, make a list of the subproblems you considered while solving them. Discuss how a computer might be programmed to solve each of the given problems, and how each of the problems might be represented to the computer. If you find a state-space representation for a problem, estimate the size of the state space and try to identify heuristics and algorithms the machine could use to search it. If computer time is available to you, choose a problem and try to implement a computer program that can solve it.

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A B C 2 Start 3 2 Goal 3 A B C