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(10 p) The 8-puzzle consists of eight numbered, movable tiles set in a 3x3 frame. One cell of the frame is always empty thus making it possible to move any adjacent numbered tile into the empty cell, or, we could say, to move the empty cell left, right, up, or down. This move has a cost of 1. Two configurations of tiles are given in the following. Consider the problem of changing the initial configuration into the goal configuration. 243 168 57 1/23 48 5 6 7 goal start Consider the following heuristic to be used with the A* algorithm: h* = the number of misplaced tiles. (a) Prove that h* is an admissible heuristic. (b) Prove that h* is also a consistent heuristic. (c) Use the heuristic h* to find an optimal path from the start node to the goal node, and justify why it is an optimal solution