You are asking the candidate to compartmentalize their thoughts to solve a toy problem during a period of time when they are attempting to put various nascent clues about your organization together in order to form a better understanding and to identify how they can provide value / fit into the flow.

Fizz-buzz tests have their place, but I think an onsite interview is past that point. In general I have found that white board exercises don't allow me to either understand or convey how I can apply my expertise to provide value for the organization.