This sliding puzzle game is played on an M*N grid, consisting of numbered squares (1..(M*N-2)), with two squares missing. The goal of the game is to move from a given initial state of the grid to a given goal state, using the smallest possible number of moves. In each move, one numbered square can slide to the place of an empty space (and in turn reveal another empty space of its old position).

Three valid states. States (b) and (c) can both be reached from state (a) with one move.

(1). Define a state, the state space of the problem and the rules for moving from state to state

(2). Propose a heuristic function to choose the next best state

(a) Is the function admissible?

(b) Is the function consistent?

(c) Will your heuristic function lead to an optimal solution, if its used with A*?

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