Answering, “I don’t know,” is actually really hard. I only learned this lesson at university- at school rarely was I asked a question so directly, or one that was as difficult as those I’ve encountered in my years at Cambridge.
This starts with the interview. Walking into a room knowing that the people sat in there are infinitely cleverer and more knowledgeable than you are is intimidating to say the least. What is more, it is completely okay to be intimidated by it, although you are unlikely to realise that when you are sitting on the waiting chair outside. Outside, I could hear the boy inside talking- to me he sounded confident, smart and much better than I thought I would ever be. The panic set in a bit- why am I here? I don’t know anything! How on earth am I supposed to answer these questions?
The reality is, you’re not supposed to “answer” them in the conventional sense, like at school. Yes, if you’re going for a science degree there probably is a correct answer, but they’re unlikely to really care what it is. If you get it, great, they’ll just ask you something harder. (They already know the answer, why on earth would they need you to tell them?) Do attempt to find it bizarrely comforting that whatever you say, they will be able to ask you something more difficult.
When people ask me, “What are they looking for?” about Oxbridge interviews, I generally answer that they simply want you to THINK. This can sound confusing, or enigmatic, but it’s the most accurate answer possible. Those interviewers will deliberately ask you things you won’t know the answer to, that is the (slightly twisted) fun of it. If you’re the right kind of person for the course, you’ll probably enjoy at least some of it, even if it might leave you feeling like someone has played rugby with your brain afterwards. When presented with a question in my interviews, it’s really easy to start off like a rabbit in headlights and not have a clue where it is going. Staying in this state is utterly pointless- it won’t help you in any way. So, break it down. What is this question asking? What information do I know that may be relevant here? Say it. Write it down. Ask for some paper if you want to (there’s usually a massive stack on the table anyway, I stole my interviewer’s pen without realising…). Essentially, I would say do what you want. Who cares how you figure it out? Run full tilt at the problem and have a stab at it, that’s what education is for! (I do not advise the same approach with patients). Draw a picture, write an equation, make a mind map- whatever floats your boat. There’s no point being embarrassed about how you think or figure it out, it is what it is. Have a go, be wrong and then be guided. That’s as good as rattling off everything perfectly, but significantly more interesting for you interviewer. Why be boring?