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Wednesday, January 26, 2011

surprise hanging paradox

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.
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 "surprise hanging" can't be on a 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 a Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.

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.

The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, will still be an utter surprise to him. Everything the judge said has come true.

5 comments:

Ijam Shadan said...

Indeed reasons and logic do cushioned our fear of the capital punishment. The surprise came with that knocks on the door, of which we almost intentionally forget to anticipate

Ruzanna Aniza said...

I don't know why, exactly, but this brought a smile to my face.

Hani Johar said...

my husband told me this exact story :)He's a super logical math geek and have quite few interesting stories like this one :)

redza minhat said...

a logic geek? interesting. must be having a tough time reconciling logic and faith. :)

Hani Johari said...

you don't say haha :)