Brainteasers and Puzzles

Can You Solve the Unexpected Hanging Paradox?


The Unexpected Hanging Paradox — also known by various names such as the Surprise Examination and the Surprise Drill — has stumped the most brilliant of thinkers. It has been debated in magazine articles, academic papers, and blog posts. Despite all the attention given to the topic, a definitive resolution of the paradox remains elusive.

The story, as it is typically told, is as follows:

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 Friday, since 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.

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 cannot 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, was an utter surprise to prisoner. Everything the judge said came true.

Was there anything wrong with the prisoner’s reasoning?

Where do things break down, creating a paradox? Despite years of debate, there is no consensus. There are two primary schools of thought: logical and epistemological, each of which put a different spin on what the judge meant when using the word “surprise.”

The different approaches have been explored exhaustively in such articles as the Stanford Encyclopedia of Philosophy’s “Epistemic Paradoxes,” and Timothy Chow’s “The Surprise Examination or Unexpected Hanging Paradox.” It has even inspired a song, “Jethro on Death Row” by Simon Beck. Perhaps you have additional insight to contribute to the discussion?

Abraham Lincoln liked to tell a story that poked fun at the opposite approach. As recounted in the 2012 movie Lincoln, the president said, “I heard tell once of a Jefferson City lawyer who had a parrot that would wake him each morning crying out, ‘Today’s the day the world shall end, as scripture has foretold.’ And one day the lawyer shot him — for the sake of peace and quiet, I presume — thus fulfilling, for the bird at least, his prophecy.”

After much head-scratching, the official Commonplace Fun Facts conclusion to the Unexpected Hanging Paradox is that the prisoner would have saved himself — and us — a lot of headaches if he would have just kept out of trouble in the first place. Let this be a lesson to you, boys and girls, that there is no such thing as a victimless crime. Now we’re all suffering because of the misdeeds of this unnamed convict.

Think you have a solution to this paradox? Let us know.

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