A prisoner is told that he will be hanged on some day between Monday and Friday, but that he will not know on which day the hanging will occur until it is due to happen.
He reasons to himself that he cannot be hanged on Friday, because if he were still alive on Thursday night, he would know that the hanging will occur on Friday; but he has been told he will not know the day of his hanging in advance.
For the same reason, he foresees that he cannot be hanged on Thursday, because if he were still alive on Wednesday night, he would know that the hanging will occur on Thursday.
Using the same argument, he foresees that he cannot be hanged on Wednesday, because if he were still alive on Tuesday night, he would know that the hanging will occur on Wednesday.
And so he reasons that he cannot be hanged on Tuesday, because if he were still alive on Monday night, he would know that the hanging will occur on Tuesday.
Hence, the hanging cannot be on Monday as well, because he now knows that the hanging will occur on Monday; but he has been told he will not know the day of his hanging in advance. Joyfully, he concludes that he will not be hanged.
Nevertheless, the executioner unexpectedly arrives on Thursday, surprising the prisoner. The statement is true after all.
Source: wolfram.com
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11 December 2007
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