The context is more like this: we regularly have internal brainstorming sessions when we run up an interesting or tricky problem, to come up with ideas on how to solve it.

So in the context of an interview, I'm trying to treat the interviewee like a colleague who I'm coming to with a problem I'm having, so we can come up with a solution together. That often involves drawing things out on a whiteboard: not code, but more diagrams to describe the problem. Then we come up with ideas on how to do it, under various constraints that I share.

Usually I have in my pocket 2-3 different approaches that we tried when we did it ourselves, and I'm looking for: can you understand the tradeoffs between these different approaches, do you understand how they work, and are you capable of implementing them to test and cross-compare them?