(If you've seen this puzzle before, don't spoil it for the others...and no googling. )


A prisoner stands before a judge. The Judge says, "There is only one punishment fit for your crimes....death by hanging. The only discretion I have is when I hang you. I'm tempted to have you hung immediately...but that would not give you sufficient time to contemplate your impending doom. I therefore command the following: You will be hung at sunrise on any of the seven days next week. I will instruct the hangman that you are not to be pre-warned about which day it's going to be. Thus, on the morning of the day you are to be hung, it will come as a complete surprise to you."

On which day(s) can the prisoner be hung?

Question if I may ?
This guy who is getting hung isn’t getting hung because he shot that squirrel that kept running around the tree is he ?

My guess is he can be hung on only one day and I think it has to do with the # 7 But not sure , there seems to be something missing but I am not the greatest At these puzzles , so I look forward to the answer.

He both shot and ate the aforementioned squirrel....but that's not why he's being hung.

None, he'd always be expecting it.

No offense CC but I don’t think that’s it ! The judge says he wants him to
have time to contemplate. But what do I know , I don’t have the answer.

CC is correct (IMHO), depending on how you read the puzzle. It's like the infamous Monty Hall problem in that the terms are ambiguous--does "it will come as a complete surprise to you" come as a condition of the puzzle, or is it merely the judge's expression of the consequences he intends?

It is both.

My humble apologies to you CC.

Explain.

The execution cannot be left until the seventh day. If it were, the prisoner would wake up knowing that he will be executed that day, violating the surprise condition. So he knows that he must be executed some time in the first six days. But the execution can't be left until the sixth day because, since he knows it can't be the seventh day, it wouldn't surprise him to be executed on that day. So he knows he must be executed sometime in the first five days. Lather, rinse, repeat.

If he reasoned that way, would it be surprising to him if he were executed on Tuesday?

Only if he was shot by Godel's Incompleteness Theorem.

Would that make him completely surprised?

That depends on what the meaning of "complete" is.

Is this related to the proof that there are no uninteresting numbers?

Anyway, that's the thing about this scenario. Obi's completely correct. He can reason that there is no way that the Judge's order can be carried out and still comply with the condition of surprise.....that being said, it is also the case that IF he is executed, any day they execute him will come as a surprise.

Call me weird, but I enjoy thought-experiments like this.

Max, you are weird.

huh?

FJ