The amount of mathematical structures and transformations you can apply (the possible rules) is effectively infinite. Simply remembering the rules might work at first, but you'll soon run into the combinatorial explosion: https://en.wikipedia.org/wiki/Combinatorial_explosion

You could go a step further, and simply say "well, ok, then the LLMs are merely doing some form of incremental/heuristic search!". Yes, but at that point you'd also be hard-pressed to claim that humans themselves are doing anything beyond that. You run out of naturalistic explanations.