In other words, BFS over the state space of the puzzle, skipping previously-visited states?
You don't actually gain anything by unrolling everything ahead of time; it'd actually be worse because you'd store all the memory and wouldn't stop when you get to the solution. And you can't really factor the state space into subproblems.
Anyway, for this puzzle BFS would work, but classical planning in general gets astronomically exponential fast. It's a neglected field, not yet thawed from the last AI winter.
You don't actually gain anything by unrolling everything ahead of time; it'd actually be worse because you'd store all the memory and wouldn't stop when you get to the solution. And you can't really factor the state space into subproblems.
Anyway, for this puzzle BFS would work, but classical planning in general gets astronomically exponential fast. It's a neglected field, not yet thawed from the last AI winter.