Unexpected hanging paradox

Started by the-pi-guy, Nov 16, 2014, 02:50 AM

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the-pi-guy

Nov 16, 2014, 02:50 AM
I have absolutely no idea why I was thinking about this at like 1 in the morning, but I wanted to share the story of the Unexpected Hanging paradox.  Try to have some fun with it. 

The Problem:

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.

Pi-guy questioning: What day will he be hung?

The solution:
Spoiler for Hidden:
Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the &quot;surprise hanging&quot; can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.<br /><br />He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.<br />

The resolution: 
Spoiler for Hidden:
The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.<br />


Pi-guys statement:
Spoiler for Hidden:
Honestly I find the backwards time logic weird.&nbsp; <br />I understand it and I get the logic, but it just feels backwards to me.

Thoughts?

BasilZero

#1
Nov 16, 2014, 02:53 AM
So he got hanged on Saturday.

Legend

#2
Nov 16, 2014, 05:01 AM
It's because the judge can fail.

Friday is a no go, but thursday is good. That morning he could be killed thursday or not at all.
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