In a prison, every prisoner has either a red dot or a blue dot on their back. They can see everybody else's dot except their own. They can't exchange information by any means, nor do they have a mirror. On day one, the director told them that those who will tell him they are wearing a blue dot at noon will be let go if it is true (else they will be executed). As it so happens, all 50 prisoners are wearing a blue dot. One afternoon, a journalist comes in and publicly asks the director, "Why are some prisoners wearing blue dots?" (publicly means that everyone can hear the question). Prove by induction that every prisoner will leave 50 days after the journalist's talk.