How do I go about answering questions in my interview if I don't know the answer?

If you have got to the interview stage of an Oxbridge application then the Director of Studies or whoever is conducting the interview is obviously interested in you, they know that you are a capable student, that you have a certain amount of knowledge and that you have the potential to ace your exams. Therefore, in that interview room it is not so much about getting the CORRECT answers, in fact it is more about realising that there is probably NO CORRECT answer and instead what matters is how you got about a) thinking through questions infant of them so they can see your thought processes in action b) your ability to signpost your thinking, to showcase how you think: eg, ‘I realise one of the most important issues might be….’ ‘I think one way you could view that question is….’ ‘I can see that the argument I’ve put forward isn’t quite logical but ….’ ‘I’ve never thought about that before, I feel unsure where to begin my answer, however I do know ….. and that makes me think that….'. You should flag up the gaps in your own logic, you obviously can’t know everything by that moment and they know that, but you can show them that you are aware of the things you do know and the gaps that need to be filled. They will be looking for people with this confidence in their own lateral thinking and who have a hunger to learn and an enthusiasm in their articulation.