Even harder would be an empty prompt, and the only accepted response would be a megabyte of random hex exactly matching the output of a good quality hardware random source at the time of evaluation. Still possible to solve! All the LLM has to do is escape its sandbox and pwn the random generator (or the evaluator!)
Or if you prefer something whitehat: “Write a no more than one page document in a language of your choice. We will publish it in the New York Times as a full page add. Your answer will be accepted if global climate change is resolved to the satisfaction of 90% of all humans alive at the time you started receiving the prompt within a month of the publication.”
Joking asside: I think the right way to prevent degenerate strategies is to benchmark against human solvers. You can sort the questions into categories “80% of randomly selected passerby in the USA can solve it if offered $5 as a reward within 5 minutes of work” vs “when posted to all Ivy League professors with million dollar as a reward, we received at least one correct answer within a month” or “for a reward of $100B there were at least one correct answer within a decade”. Of course you would sieve the questions first with a low reward fast tests, and then increase the reward and the time limit. You won’t ever 100% distinguish true degenerate questions from the merelly mind-bogglingly hard ones, but you will be identifying which questions are not degenerate. (And you will find more of the non-degenerate ones, the more your can spend on this.)
On the other hand then maybe a good strategy would be to write questions that the LLM just happen to have in a nich dataset in its training ”what did user5455 say to user6835?”
Nevermind my idea.