What can be the efficient approach to solve the 8 puzzle problem?

Question

The 8-puzzle is a square board with 9 positions, filled by 8 numbered tiles and one gap. At any point, a tile adjacent to the gap can be moved into the gap, creating a new gap p

Answer 1

You can use the heuristic that is based on the positions of the numbers, that is the higher the overall sum of all the distances of each letter from its goal state is, the higher the heuristic value. Then you can implement A* search which can be proved to be the optimal search in terms of time and space complexity (provided the heuristic is monotonic and admissible.) http://en.wikipedia.org/wiki/A*_search_algorithm