Logic and math · experts disagree
The unexpected hanging
Circulating since the 1940s; first discussed in print by D. J. O'Connor (1948) and made famous by Martin Gardner.
A judge tells a prisoner on Saturday that he will be hanged at noon on one of the five weekdays to come, and that the day will be a surprise: he will not know on the morning of the hanging that it is the day. The prisoner goes back to his cell and reasons it out. It cannot be Friday, because if he is still alive on Thursday afternoon, Friday is the only day left and would be no surprise. With Friday ruled out, it cannot be Thursday either, by the same argument, and so on back through the week. He concludes, with relief, that the sentence cannot be carried out.
On Wednesday at noon the hangman arrives, and the prisoner is entirely surprised. Where did his reasoning go wrong?