A logic puzzle that first became known by word of mouth in the early 1940s.
One form of the paradox is the following:

A prisoner has been sentenced on Saturday. The judge announces that "the hanging will take place at noon on one of the seven days of next week, but you will not know which day it is until you are told on the morning of the day of the hanging." The prisoner, mulling this over, decides that the judge's sentence could not possibly be carried out. "For example," he thinks, "I can't be hanged next Saturday, the last day of the week, because on Friday afternoon I'd still be alive, and I'd know for sure that I'd be hanged on Saturday. But if know this before I'm told about it on Saturday morning, this would contradict the judge's statement. So they won't hang me on Saturday" And they couldn't hang him on Friday, because he knew he wouldn't be hanged on Saturday; so on Thursday, he'd know that Friday would be the last chance for an unexpected hanging -- but it wasn't unexpected anymore! In the same way, he argued, they could not hang him on Thursday, or Wednesday, Tuesday, or Monday. "And they can't hang me tomorrow," thought the prisoner, "because I know it today!"

And then they hang him tomorrow, and he doesn't expect it at all because of the above reasoning.