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Not that I advocate this approach, but another way to look at FizzBuzz is as a personality test.

If a (senior) developer balks at writing FizzBuzz, perhaps it shows arrogance and a lack of humility. It could also be useful to see if the developer follows up to inquire as to why they were asked a FizzBuzz question, and about its relevance to the work. I see this kind of questioning as not only fair game, but good to ask about. Not asking about something that seems out of place could seem off.