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The Surprise Execution Paradox


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15 replies to this topic

#1 megamatt

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Posted 26 June 2007 - 10:57 PM

My roommate in college told me this one:

A man in the old west is found guilty of a crime. At his sentencing on a Sunday, the honest judge tells him this: "You are found guilty and are sentenced to death by hanging. You will be hung at high noon one day this week. However, the day of your hanging will be a complete surprise to you, and you will not know if it is the day until the morning of that day."

Later in council, his attorney tells him excitedly, "You've gotten off! There is no way the sentence can be carried out and the honest judge keep his word! You see, there is no way you can be hung on Saturday, because it's the last day of the week, and you'll know Friday night that your hanging will happen the following day, that makes Friday the last day you can be hung. But that can't be, because then you'll know when Thursday night rolls around that you'll be hung on Friday, because its the last day. But then you'll know Thursday, so you cannot be hung Friday, making Thursday the last day, and so on until today!"

The man, having heard this, confidently strolls to his jail cell having just avoided a death sentence. But when he is pulled out of his cell Tuesday morning to be hung at noon, he is 100% surprised!
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#2 undeniable

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Posted 27 June 2007 - 08:16 PM

could it be that the noon the judge is talking about is noon somewhere else, after all it is high noon somewhere all the time. (or it could be midnight)
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#3 sarcasticblonde

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Posted 29 June 2007 - 11:19 PM

At his sentencing on a Sunday, the honest judge tells him this: "You are found guilty and are sentenced to death by hanging. You will be hung at high noon one day this week. However, the day of your hanging will be a complete surprise to you, and you will not know if it is the day until the morning of that day."

Later in council, his attorney tells him excitedly, "You've gotten off! There is no way the sentence can be carried out and the honest judge keep his word! You see, there is no way you can be hung on Saturday, because it's the last day of the week, and you'll know Friday night that your hanging will happen the following day, that makes Friday the last day you can be hung. But that can't be, because then you'll know when Thursday night rolls around that you'll be hung on Friday, because its the last day. But then you'll know Thursday, so you cannot be hung Friday, making Thursday the last day, and so on until today!"

The man, having heard this, confidently strolls to his jail cell having just avoided a death sentence. But when he is pulled out of his cell Tuesday morning to be hung at noon, he is 100% surprised!



The problem is there is a lawyer trying to use logic.
He is right, but only to a point. Yes, if he had not been hung by Saturday, then it would not be a surprise on Saturday morning as that was the only day left. The judge started off the sentence telling him he would be hung one day this week, so the fact he is being hung isn't a surprise -- only the day. So if you rule out Sunday (the day of the sentence) and Saturday (for reasons noted above), there are five possible days. On Monday, he has a 20% chance of being hung. If that doesn't happen, then on Tuesday, he has a 25% chance of being hung. On Wednesday, 33.3%, On Thursday, 50%, and if lasts till Friday, 100%.
The last day he always has 100% chance. So if you try to keep backing the day up using the lawyer's logic, you end up with Monday being 100%.
If you are using the logic that the judge is honest in saying it will be a surprise, you must also use the logic that he is honest in saying it will happen one day this week.
And ... he was surprised, right? And he was hung, right? So the judge was right.

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#4 quoteable

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Posted 02 July 2007 - 07:29 AM

I first saw this in a book by Martin Gardner called (I think) Mathematical Puzzles and Paradoxes.
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#5 unreality

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Posted 09 July 2007 - 04:20 PM

so did i. Martner Gardner explained the solution to the faulty logic, too. The lawyer reasoned wrong because you can't even be sure if the VERY LAST DAY is the hanging day, even if all days before it have gone by and you havent been hung. It's explained with this:

There is a husband and a wife. The wife's birthday is tomorrow. Her husband says: "For your birthday tomorrow I'm going to get you an unexpected gift. You'll have no idea what it is until you open it... It will be that gold necklace we saw in the jewelry store."

The wife knows her husband to be truthful, but this confused her. The more she thinks about it, the more confused she is. Her husband made two statements there: the gift will be unexpected, AND the gift will be the golden necklace. Since both couldnt be true her husband isnt being truthful, he has to be lying. So he might get her the golden necklace. Or he might get her that new vacuum cleaner they need. Who knows. She has no idea.

The next day she opens her gift and its the golden necklace from the jewelry store. It is both unexpected AND the golden necklace. Her husband was being truthful all along, and he knew it. She didn't until she opened it though.

In this way even if the last day possible for the hanging is tomorrow, we cant be sure if it will happen.
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#6 bonanova

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Posted 20 July 2007 - 08:08 AM

Putting it another way, the more certain the man is
[on Friday night, should he live that long] that he
cannot be hanged on Saturday [the last possible
day for the hanging] the more surprised he is
when it happens. It's possible because of the
prisoner's unwavering belief in the truth of the judge's
statements.

As with other semantic paradoxes, the assumption
that what is being asserted is true comes into play.
If the prisoner didn't believe what the judge said
was true, he might [expectantly] dread a Saturday
hanging, thereby precluding it!

The moral:
Never believe a judge. It might cost your head.


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 BoilingOil

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Posted 26 September 2007 - 08:48 PM

The problem is there is a lawyer trying to use logic.
He is right, but only to a point. Yes, if he had not been hung by Saturday, then it would not be a surprise on Saturday morning as that was the only day left. The judge started off the sentence telling him he would be hung one day this week, so the fact he is being hung isn't a surprise -- only the day. So if you rule out Sunday (the day of the sentence) and Saturday (for reasons noted above), there are five possible days. On Monday, he has a 20% chance of being hung. If that doesn't happen, then on Tuesday, he has a 25% chance of being hung. On Wednesday, 33.3%, On Thursday, 50%, and if lasts till Friday, 100%.
The last day he always has 100% chance. So if you try to keep backing the day up using the lawyer's logic, you end up with Monday being 100%.
If you are using the logic that the judge is honest in saying it will be a surprise, you must also use the logic that he is honest in saying it will happen one day this week.
And ... he was surprised, right? And he was hung, right? So the judge was right.



I would guess you aren't as blonde as you are sarcastic . Don't take that the wrong way, though. It's perfect.
I wouldn't be too sure about the maths in your assessment of the situation, although I can't see a way of disproving it. But the situation is simply that he WAS hung some day that week, as the Judge promised, and it WAS a surprise to him, also like the Judge said...

Actually, what the lawyer said also made good sense. It was all perfectly logical. BUT that only gave the man the certainty he would not hang, and THAT made the surprise complete. After all, he was convinced he would not hang, but he did!

What else is there? An eternity in hell for this man


BoilingOil
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#8 spoxjox

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Posted 11 December 2007 - 12:04 AM

Pitiful attempts at off-color humor notwithstanding (and there are always some), people who are executed by hanging are hanged, not hung. The judge may have been honest, but his grammar was substandard.
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#9 Eugenia

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Posted 10 February 2008 - 01:22 AM

Huh, I think i just replyed the the same question yeserday, only about a math teacher and student predicting a drop quiz. I don't think this is paradox really, yet to some extent it is - you could say that the guy's lawers resoning is. Oh, here it is! - that one about the math teacher...:
Predicting a Drop Quiz
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#10 cm0265880

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Posted 27 February 2008 - 08:03 AM

Maybe the judge forsaw the flawed logic in his own ruling. He predicted the reactions of the condemed man and his lawyer alike. He gave them a sure outcome in thier favor using deductive reasoning. A false sense of security that only reason could secure. He wanted to give them a concrete belief that the condemed man's execution wasnt logically possible therfore making his actual execution a complete suprise. If the condemed man thought that he could actually be exucuted sometime during the week then he would be expecting the act to occur and would in at least some way be unsuprised. The judge used logic to predict the best way to carry out the sentence. The judge demonstrates how a persons own logic can be there downfall.
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