Lucky you.
> Programming is essentially a detective work of high level problem solving.
Agreed. What are the questions you ask to determine their detective abilities?
It can show the ability to read code, experience with any language or framework footguns, how to work with a malspecified problem (it is S.O. after all), etc, depending on the kinds of risks the screen is trying to drive down in your specific team
in my experience, talking to a candidate across a couple of rounds and asking some generic question that can create discussions, will get some answers. sometimes, designing a system together can help a lot (as always reminding the candidate that there are no wrong answers).
at the end of the day, interviewing is a flawed process and you will get it wrong -- the question i don't see being asked is: what do you do if you get wrong?