When you're solving the sliding cars puzzle as a person you're not thinking of graphs. The experience of solving OP's puzzle is entirely different from the one you mention. In theory you could stop, write down the underlying graph representation and solve it that way I suppose. Does anyone do that though?
You’re correct. (As I mentioned, having the explicit graph makes it easier, and as another person mentioned, this makes it an essentially different problem.) I wasn’t meaning to say that it’s identical. Just the closest thing I could think of offhand. When I was in grad school working on problem solving we used to make up new problems every day. Every little change changes the problem’s affordances, but if you define a problem type by the method of solution, all of this class are isomorphic (along that dimension). Again, none of this is to take away from the fun design of this problem.
