I think that asking really simple fizz buzz style questions in this context is probably fine. The whole point I think is to screen out candidates who can't do t

I think that asking really simple fizz buzz style questions in this context is probably fine. The whole point I think is to screen out candidates who can't do these sorts of assignments in ~5-20 minutes or whatever. With a take home assignment you'll get people who spend two hours or on your 15 minute problem which is the kind of person who I think OP is trying to filter out. I think even if you're not the kind of person who can think on the spot with someone watching you well, you should be able to knock out fizz buzz style question in that setting quickly.