I\'ve read in one of my AI books that popular algorithms (A-Star, Dijkstra) for path-finding in simulation or games is also used to solve the well-known \"15-puzzle\".
Remember that A* will search through the problem space proceeding down the most likely path to goal as defined by your heurestic.
Only in the worst case will it end up having to flood fill the entire problem space, this tends to happen when there is no actual solution to your problem.