This work is interesting. I wouldn't have guessed 3x3 puzzles would be solvable by a large Markov chain. It would be interesting to know how large of a context is necessary to solve 9x9 puzzles. No existing model can currently solve 9x9 puzzles even though the recursive backtracking algorithm can solve any given puzzle in less than a second.
As others have pointed out, maybe intelligence derived from language just isn't very good at math? It's not like linear algebra comes naturally to humans, we have to be specially trained. I've been taking Khan Academy classes and believe me, math sure doesn't come naturally to me.
I realize tempers are high on this subject, but I literally just wanted to point it out, in case you hadn't seen it. I wasn't trying to dunk on you or anything.