James, Getting off topic but, I recently heard a few of these questions at "escape rooms" from actors while trying to solve puzzles and realized how frustrating some are. Maybe our students feel the same way:
What is the answer? I'm aware that I'm trying to get an answer - this is an infuriating question.
Does this answer make sense? Folks either do their own standard sanity checks or need you to point them toward a check that they haven't thought of. I'd prefer "What's the limiting case of ... " or "WRONG".
What question might this lead us to ask? I think the goal here is to get someone to verbalize their thoughts. Maybe a better way to achieve that is a less interrogative "Talk me through your thoughts on X so I can help"
Is there a pattern here? "I OBVIOUSLY don't know, or I would have solved it". Give me a hint or leave me alone.
How convinced are you? AKA "are you sure?" Maybe I'm poorly socialized, but I take this as epistemological. Probably not the discussion anyone wants to have.