What do I do if I don't know the answer to the professor's question?

Don't worry, they are doing this on purpose! Oxbridge interviews aren't meant to trick you, but they are meant to test how you cope with new information and working things out on your own.

The interviewer wants to see how you reason and think about issues. Take your time and talk through the issue. Ask questions if you need to clarify a point. Take small steps that show how you would try and get close to the answer. Don't worry about going wrong or making mistakes, but if you do realise you are going down the wrong track then say so! Don't try and pretend that you're right when you know otherwise - awareness is a much more highly prized skill in Oxbridge interviews!