#5 – The unexpected hanging paradox or hangman paradox
via www.geoffwilkins.net complain
A judge tells a condemned prisoner that he will be hanged at noon on one day in the following week, exceprt the weekends; but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner enters his cell. 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 last day in week. 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. In addition, 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 enters the prisoner's cell at noon on Wednesday — which, despite all the above, will still be an utter surprise to him. Everything the judge said has come true.
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