They don't have 9x9 puzzles. Any guesses as to why they only tried 3x3, 4x4, and 5x5 but not 9x9?

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.