> "Consider a theoretical world where people who are shorter always have bigger feet. Ben is taller than Paul, and Paul is taller than Andrew. Steve is shorter than Andrew. Everyone walks the same number of steps each day. All other things being equal, who would step on the most bugs and why?"

Because Ben is the tallest, his feet are the biggest, and because he takes the same amount of steps as the others, the amount of area he steps on is larger than the area that the others step on.

Therefore Ben is most likely to be the one to step on the most bugs.

Easy. And I'm not brilliant.

The problem with testing these tools is that you need to ask it a question that is not in their training sets. Most things have been proven, so if a proof is in its training set, the LLM just regurgitates it.

But I also disagree: if the "AI" can't reason about that, it can't reason because that one is so simple my pre-Kindergarten nieces and nephews can do it.

But even if not, the LLM's should have "knowledge" about exponential functions and factorial because the humans who wrote the material in their training sets did. So it's not a lack of knowledge.

And I claim that most humans could rediscover theorems from basic axioms; you've just never asked them to.