A judge promises a surprise execution next week. Logic seems to rule out every day.
A prisoner is told he'll be hanged at noon on one weekday next week, but that the hanging will come as a total surprise — he won't know the day until the executioner knocks. He reasons his way through it, day by day. Can you follow his logic, and see where it goes wrong?
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He reasons backward: it can't be Friday, the last possible day, because if he's still alive Thursday night he'd know it must be Friday — no surprise. But with Friday eliminated, the same logic then rules out Thursday, then Wednesday, and so on back to Monday — seemingly proving the judge can't keep his promise at all. Yet the executioner then knocks on, say, Wednesday, and the prisoner is genuinely surprised, since his own 'proof' had already convinced him it was impossible. Philosophers have never reached consensus on exactly where the prisoner's reasoning breaks down; Martin Gardner brought the paradox to wide attention in his March 1963 Scientific American column.