The Unexpected Hanging

[Kalkewl8ter]

This is more of a logical paradox than math, but it's still rather interesting:

A prisoner has been sentenced to death, and the jailer tells him this: "You will be hanged one day next week between monday and friday inclusive, but you will not know which day until the morning of that day."

The prisoner is delighted to hear this, because he can logically deduce that he will not die from the jailer's statement. He can't die on Friday, because if he is still alive on Thursday afternoon, he will already know that he is going to die on Friday when it's only Thursday, and, according to the jailer, he can't know until the morning of the hanging. He then decides that if he is still alive on Wednesday, he can now only die on Thursday or Friday, but Friday was already eliminated, so he would know that he would die on Thursday, when it's only Wednesday. So now, he can't die on Thursday. Similarly, he rules out all the days of the week.

However, as the prisoner is waiting happily in his cell Thursday morning, positive he won't die this week, the jailer comes and tells him that the hanging will be this afternoon. Now the prisoner will be hanged unexpectedly, just as the jailer had originally stated. And the jailer's statement is valid again.

So was the prisoner right in his deductions that he can't die, when real life so obviously contradicts him???

[bugzpodder]

the story doesn't make much sense to me execept that it is not thursday yet so the prisoner won't know that if he'll be alive by thursday, so he'll have no way of ruling out friday, and similarly ruling out any day of the week.

[bugzpodder]

let me clear up my explaination (sorry i tend to be annoy when it comes to math ): the prisoner's deduction that he can't be killed by Friday is solely based on the assumption that he hasn't been killed by Thursday.

If indeed this is true, then the prisoner's logic seems to be agreeable. but keep in mind that he cannot be killed on monday to thursday (since he is alive on thursday afternoon according to the assumption, killing him early would be out of the question)

[DavidHooper]

the prisoner's deduction that he can't be killed by Friday is solely based on the assumption that he hasn't been killed by Thursday.

You hit the nail on the head bugz.

[hypnos]

I love reading these kind of word games Let's consider this scenario; the jailer was lying, walks in to the jail on Monday morning with a revolver in his hands - then the prisoner would be up shi* creek in a barbed-wire canoe.

The trouble with these though is that we're assuming English is being used in an absolute and logical manner. In reality though, English is used more loosely...I don't suppose you could rewrite this story about the prisoner and the jailer in Maths talk could you?

Nah only joking, it's quite good. Where'd you read it or did you make it yourself?

[Kalkewl8ter]

Ok, the story might have been a bit vague, but when the prisoner said he couldn't be killed on Friday, it was because he would have been alive on Thursday IF he were to be killed on Friday.

[bugzpodder]

http://www.greylabyrinth.com/Puzzles/answer051.htm
for a solution

[Kalkewl8ter]

Good solution, Bugz!
The original place that I got the example from was The Colossal Book of Mathematics, by Martin Gardner.