Quote Originally Posted by Jonax View Post
I guess for small puzzles like 3x3 brute force could do it, or some clever algorithm.
I doubt brute force approach would be very effective here. Why? To many chances to end up repeating same sets of moves within a loop which could then end up in endless cycle.

Quote Originally Posted by Jonax View Post
Wouldn't be surprised if those already exist somewhere.
Of course they do exist. One of the most common mentioned algorithm for solving Sliding puzzles is Iterative deepening A* algorithm: https://en.wikipedia.org/wiki/Iterative_deepening_A*