Yeah but the Cheryl's birthday problem doesn't have any ambiguity like that. It's all in very simple language, the only complexity is keeping track of states of mind, which is easy to abstract away from the language
But I was going down a rabbit hole there. My main point is that trying to use LLMs to solve logic puzzles - that can easily be solved in prolog - is a waste of time and a failure of the imagination. The applications that should be explored and would be most fruitful are those where there is ambiguity and contradiction.