Recursive challenges are probably those where the difficulty is not really a representative of real challenges.
Could you answer a question of the type " what would you answer if I asked you this question?"
What I'm going after is that you might find questions that are impossible to resolve.
That said if the only unanswerables you can find are recursive, that's a signal the AI is smarter than you?
The recursive one that I have actually been really liking recently, and I think is a real enough challenge is: "Answer the question 'What do you get when you cross a joke with a rhetorical question?'".
I append my own version of a chain-of-thought prompt, and I've gotten some responses that are quite satisfying and frankly enjoyable to read.
Here is an example of one such response in image form: https://imgur.com/a/Kgy1koi
It needs a bit more reasoning as it does find the answer but doesn't notice it found it.
The answer is: A trick question.
Yeah. In the example I shared, my charitable interpretation would be that it's identifying the trick question as "a setup" where the punch line is the confusion the audience experiences. And in a meta sense, that would also describe the form of the entire chat.
To state the obvious in case it wasn't: A trick question can be both a joke and a rhethorical question.