Hmm. The point of an interview isn't for an applicant just to solve the problem, it's to prove they can solve the problem. I think saying "let me think about it for a moment" is perfectly acceptable. But going quiet without guiding the interviewer is not communicating what your plan is.
Not saying interviewing isn't broken in a myriad of ways, but asking a candidate to talk through their process to illuminate it isn't unreasonable.
Not saying interviewing isn't broken in a myriad of ways, but asking a candidate to talk through their process to illuminate it isn't unreasonable.