Yes I think it depends on how you definite permutations for this puzzle. For example, if you limit your goal to training GPT to solve puzzles of the form where there only ever 3 distinct real animals, then my claim is that you wouldn't need to feed it examples of this puzzle with every single permutation of 3 different animals (assuming 10000 different animals that is already over 100bn permutations) before the neural network developed an internal logical model that can solve the puzzle as well as a human. It would only need a few descriptions of each animal plus a few examples of the puzzle to understand the logic.
If you mean to say that the permutations of the puzzle extend to changing the rules such as "if it's the Sabbath then reptiles can't travel" then sure it would require more representative examples and may never meet your standard of "error free" but I would also argue the same applies to humans when you present them a logic puzzle that is new to them.
> you wouldn't need to feed it examples of this puzzle with every single permutation
No, but you would need "enough"; whatever that number happens to be.
> It would only need a few descriptions of each animal plus a few examples of the puzzle to understand the logic.
That's the mistake.
GPT itself can't combine those two things. That work has to be done by the content of the already-written training corpus.
And the result is not the same as "understanding logic". It doesn't model the meaning of the puzzle: it models the structure of examples.
GPT can't distinguish the meaning of rules. It can only follow examples. It can't invent new strategies, it can only construct new collections of strategy parts; and it can only pick the parts that seem closest, and put those parts into a familiar order.
If you mean to say that the permutations of the puzzle extend to changing the rules such as "if it's the Sabbath then reptiles can't travel" then sure it would require more representative examples and may never meet your standard of "error free" but I would also argue the same applies to humans when you present them a logic puzzle that is new to them.