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.
By systematic (BFS) search of the entire 32-state space under these rules, one finds no path from to that stays always safe. Thus the puzzle has no solution—there is no way for the man to ferry all four items across without at least one of them being eaten.
O3 gave me basically that solution. "Below is the shortest safe schedule that really works ‒ but it assumes the boat can hold the man plus two passengers (three beings total). If your version of the puzzle only lets him move one passenger at a time, the puzzle has no solution: at the very first trip he would always leave at least one forbidden pair alone."
I don't have access to Think, but I tried Grok 3 regular, and it was hilarious, one of the longest answers I've ever seen.
Just giving the headings, without any of the long text between each one where it realizes it doesn't work, I get:
Solution
[... paragraphs of text ommitted each time]
Issue and Revision
Revised Solution
Final Solution
Correct Sequence
Final Working Solution
Corrected Final Solution
Final Correct Solution
Successful Solution
Final answer
Correct Final Sequence
Final Correct Solution
Correct Solution
Final Working Solution
Correct Solution
Final Answer
Final Answer
Each time it's so confident that it's worked out the issue, and now, finally, it has the correct, final, working solution. Then it blows it again.
I'm surprised I didn't start seeing heading titles such as "Working solution-FINAL (3) revised updated ACTUAL-FINAL (2)"
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.