Sure - but you're not likely to really see the "real" thought process you're hiring for by asking a stranger a riddle you already know the ansewr to in a high-pressure situation.
Real problem-solving and thinking is done in a huge number of ways that sometimes isn't conducive to strangers, pressure, or whiteboarding.
> I'm interested in when candidates pick not-optimal choices for good reasons
Right - which is why starting with something they've written on GH (which is something they've thought about and are probably passionate about) is a great jumping-off point for such a convo.
> As an aside, the reason not to work on novel-to-you problems with job-seekers is that it's very hard to fairly compare candidates after.
I see your good-intention here, but it's nearly impossible to compare two candidates without all kinds of biases (implicit and explicit) coming into play.
> I strongly prefer pairing on the same problem with all the candidates in a batch. Otherwise it's hard to tell if a bad result is due to a bad problem or an unacceptable candidate.
I think this may be another way of trying to compare candidates to eachother (which is perilous).
Good candidates can do well with bad questions, and bad candidates can rarely do better than okay with good questions. There are lots of good/proven questions you haven't solved - ask your colleagues.
As an aside, the reason not to work on novel-to-you problems with job-seekers is that it's very hard to fairly compare candidates after. I strongly prefer pairing on the same problem with all the candidates in a batch. Otherwise it's hard to tell if a bad result is due to a bad problem or an unacceptable candidate.