If I am interviewing you, I wouldn't mind you giving me a puzzle. Depending on how you do it, I would think you are either the world's biggest asshole, or a very easy guy to work with, and that's very valuable information.
Maybe you should! You should be interviewing them as much as they are interviewing you. When they ask if you have any questions for them, respond with, "Could you solve this for me?" Then give them a programming problem.
If you're being interviewed by a non-technical person (who obviously can't program), that could be a red flag right there (in and of itself).
Good idea! Draw them the "Thinking outside the box"[1] puzzle or something.