Neat game in the link! I played it until I ran into some non-obvious ones, solved them, and then thought about what kinds of AI code might automate the solution process. When I came back here, your analogy between the game and solving math problems changed from opaque to beautiful :-)

I wonder if there is a pedagogical application? Maybe it would work as a side exercise in the intro to math/physics classes, so you could use the game plus the verbal analogy to help students vividly experience the way that playing with a tough problem for a while can be productive?