Further support for the memorization claim: I posted examples of novel river crossing puzzles where LLMs completely fail (on this forum).
Note that Apple’s actors / agents river crossing is a well known “jealous husbands” variant, which you can ask a chatbot to explain to you. It gladly explains, even as it can’t follow its own explanation (since of course it isn’t its own explanation but a plagiarized one, even if changes words).
edit: https://awful.systems/post/4027490 and earlier https://awful.systems/post/1769506
I think what I need to do is to write up a bunch of puzzles, assign them randomly to 2 sets, and test & post one set, while holding back on the second set (not even testing it on any online chatbots). Then in a year or two see how much the set that's public improves, vs the one that's held back.