A newspaper runs a competition in which every entrant guesses an integer between 0 and 100 inclusive, the winner of the competition is the person who's guess is closest to 2/3rds of the average integer guessed, what number do you guess?

If I was helping prepare a student for an oxbridge interview I would begin by reminding them not to rush into the answer, explaining that tutors want to see your logical thinking process, and that rushing in almost inevitably lands them at the wrong answer. I would get them to think through what the winning answer would be under certain scenarios such as everyone guessing randomly and everyone guessing a certain number, hopefully this highlights to the candidate the undercutting process that goes on in a competition like this. Once the candidate understands what is going on, and chooses an appropriate number, I would get them to actively discuss how this relates to economics and to bring in any of their own knowledge in this field since these are the key skills that tutors are really looking for.