I also have a question that LLMs always got wrong until ChatGPT o3, and even then it has a hard time (I just tried it again and it needed to run code to work it out). Qwen3 failed, and every time I asked it to look again at its solution it would notice the error and try to solve it again, failing again:
> A man wants to cross a river, and he has a cabbage, a goat, a wolf and a lion. If he leaves the goat alone with the cabbage, the goat will eat it. If he leaves the wolf with the goat, the wolf will eat it. And if he leaves the lion with either the wolf or the goat, the lion will eat them. How can he cross the river?
I gave it a ton of opportunities to notice that the puzzle is unsolvable (with the assumption, which it makes, that this is a standard one-passenger puzzle, but if it had pointed out that I didn't say that I would also have been happy). I kept trying to get it to notice that it failed again and again in the same way and asking it to step back and think about the big picture, and each time it would confidently start again trying to solve it. Eventually I ran out of free messages.