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.

Why are people so intent on incorrectly asserting these models are Markov chains? It makes sense to use the analogy as an educational tool for exposition, but it more often seems that many use it as a way to minimize the notion that these models could ever possibly be useful for anyone. Is this just simply to make it more intuitive for others that it's a sequence model? Because it seems about as helpful as 'email is just bits' when everyone and their grandma knows about the relation between transformers, GAT, and circulant matrices.

Well, you just said sudoku.

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.