The Paradox of the Unexpected Hanging

In the cell, the man sits down and thinks for a while about his predicament. He wonders which day would be most suitable for an execution to take place but cannot find any good reason why any particular day would be more suitable than any other. On the point of giving up and resigning himself to his fate, he suddenly has an idea. He jumps up quickly. "Fetch the judge!" he shouts out to the jailer "I'm going to be set free!" The jailer goes calmly to get the judge. When the judge arrives he looks surprised. "So," he says to the condemned man "what is all this fuss about?" "You must set me free," says the man. "Really? Why is that?" "Listen: if it comes to next Saturday and I have not been executed yet, then I'll know that Sunday is the day because there's only one day left." The judge listens as the man continues. "So that means that Sunday is ruled out because I'll be able to predict my execution on Saturday. And if Sunday is ruled out, that means that Saturday is the latest I can be executed. But by the time it gets to Friday, I'll know it has to happen on Saturday. So Saturday is ruled out too because I'll be able to predict it on Friday. And if Saturday is ruled out, that means that Friday is the latest I can be executed. By the same reasoning, all of the other days of the week can be ruled out. Therefore, by your own ruling you cannot possibly execute me." The judge goes away while the man sits back and relaxes in his cell, secure in the knowledge that he will soon be free.

 

 

(Click the poorly drawn gallows for part 3)