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The Unexpected Hanging


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#1 Haiming

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Posted 05 June 2012 - 01:51 AM

A man condemned to be hanged was sentenced on Saturday. "The hanging will take place at noon," said the judge to the prisoner, "on one of the seven days of next week. But you will not know which day it is until you are so informed on the morning of the day of the hanging."
The judge was known to be a man who always kept his word. The prisoner, accompanied by his lawyer, went back to his cell. As soon as the two men were alone, the lawyer broke into a grin. "Don't you see?" he exclaimed. "The judge's sentence cannot possibly be carried out."
"I don't see," said the prisoner.
"Let me explain They obviously can't hang you next Saturday. Saturday is the last day of the week. On Friday afternoon you would still be alive and you would know with absolute certainty that the hanging would be on Saturday. You would know this before you were told so on Saturday morning. That would violate the judge's decree."
"True," said the prisoner.
"Saturday, then is positively ruled out," continued the lawyer. "This leaves Friday as the last day they can hang you. But they can't hang you on Friday because by Thursday only two days would remain: Friday and Saturday. Since Saturday is not a possible day, the hanging would have to be on Friday. Your knowledge of that fact would violate the judge's decree again. So Friday is out. This leaves Thursday as the last possible day. But Thursday is out because if you're alive Wednesday afternoon, you'll know that Thursday is to be the day."
"I get it," said the prisoner, who was beginning to feel much better. "In exactly the same way I can rule out Wednesday, Tuesday and Monday. That leaves only tomorrow. But they can't hang me tomorrow because I know it today!"
... He is convinced, by what appears to be unimpeachable logic, that he cannot be hanged without contradicting the conditions specified in his sentence. Then on Thursday morning, to his great surprise, the hangman arrives. Clearly he did not expect him. What is more surprising, the judge's decree is now seen to be perfectly correctly. The sentence can be carried out exactly as stated.
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#2 Aaryan

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Posted 05 June 2012 - 02:01 AM

The term "expect the unexpected" applies in this case.
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#3 TheCube

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Posted 05 June 2012 - 10:27 PM

For a second I thought this was a riddle and was looking alll over for the question, lol.
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Jack and Jill went up the hill
to fetch a pail of water.
Jack fell down and broke his crown
And Jill just laughed at Jack as he sat there unconscious.

Jack should've known that Jill was a baddie . . .

#4 Haiming

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Posted 06 June 2012 - 12:46 AM

For a second I thought this was a riddle and was looking alll over for the question, lol.

^_^
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#5 bonanova

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Posted 16 February 2013 - 03:29 AM

An important question to answer is, Is the judge a reliable truth-teller?.

If the truth of a speaker's statements leads to a paradox, we might consider that he is a liar.


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

#6 Prime

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Posted 23 February 2013 - 02:38 AM

I read this one long time ago in Russian translation of one of Martin Gardner's books.

One of the conditions there is that the Judge cannot possibly lie. It is an old, very interesting twist on liars' paradox. I believe the mostly accepted solution is:

The proposition made by the judge is not decidable. Therefore, the condemned man may not derive any inferences from it. They could execute him on the very last day Saturday, and still it would be a surprize. Thus it turns out, the judge did not lie.


Edited by Prime, 23 February 2013 - 02:40 AM.

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Past prime, actually.





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