Can you solve it? Oxford university admissions questions

Brainteasers for budding philosophers

UPDATE: Solutions can now be read here.

Do you have what it takes to study philosophy at Oxford? Today's three puzzles are epistemic logic puzzles', that is, puzzles concerned with reasoning about knowledge. But I know you know I know you know that.

All three puzzles have been set in recent years during Oxford university admissions interviews for joint philosophy degrees. In each case, there is an initial question. Almost all candidates will answer this correctly, and I hope you will too. I've also included a sample of the follow-up questions. Only the best candidates will get everything right. Best of luck!