Question: Nine blocks are placed in a tray as shown below, (a) How many different configurations of the blocks may be obtained by sliding them about

Nine blocks are placed in a tray as shown below,

(a) How many different configurations of the blocks may be obtained by sliding them about in the tray?

(b) How many different configurations of the puzzle are there if configurations that may be obtained from each other by rotating or flipping the tray are considered to be the same?

(c) Design a computer program that can explore the state-space of the sliding-block puzzle.

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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