I would approach a whiteboard interview collaboratively. Generally I would leave it up to the candidate to drive the problem solving in this case, but I would

I would approach a whiteboard interview collaboratively. Generally I would leave it up to the candidate to drive the problem solving in this case, but I would expect them to ask questions and get input rather than just sit back and let them sweat. If they were going down the wrong track I might also ask questions to nudge them in the right direction. Seeing how they engage in this kind of process would be precisely what I want to understand.