I think the part that's missing from discussion here is: "First: Make sure you understand the problem". Sure, for strictly algorithmic questions, where there is

I think the part that's missing from discussion here is: "First: Make sure you understand the problem". Sure, for strictly algorithmic questions, where there is one mathematically demonstrable optimal answer (or at least, a way to compare solutions), this may seem less important, but for more open-ended questions (e.g., "How many barbers are there in [$LOCATION]?"), clarifying the why is essential, because definitions are important and vary by context. It's also important to seek whether a "good enough" solution is acceptable, or if high optimization is important. (Related, what are the memory/processing/load/runtime constraints, if any.) These are the sorts of questions that, in my mind, demonstrates a candidate's willingness to reflect on his/her own solutions.