One of my favorite interviews (Mixrank) was where the CTO/founder and I picked a random problem on Project Euler and we both coded on it in parallel. I was in the driver's seat as far as design and general approach was concerned but we were each coding an independent solution. We weren't even using the same languages.

Once we both had the correct answer, we started optimizing to try and eclipse each others' runtime. This was actually a fantastic test to display deeper knowledge beyond just regurgitating a solution, showing benefits and drawbacks of different languages and patterns, and seeing how we could work while agreeing or disagreeing on a technical subject.

I was really too junior for the role they wanted and I didn't get the job, but it was a fantastic experience.