We can solve the puzzle of my last post using a

Breadth-first search (BFS) algorithm. The key idea is to realize than the problem is just a Shortest Path problem where the graph, even when it is not completely known at the beginning (because we don't have the graph's adjacency list or adjacency matrix), can be built joining the states the board takes after every movement. The image below can help to understand this. It shows some of the states the board cab take after some movements starting from the beginning.