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The Unexpected Hanging Paradox


DonRocks

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A judge says to a prisoner: "You're going to be hanged at noon on one weekday next week, but the day of the hanging will be a surprise to you, and you will not know which day it's going to happen until the hangman knocks on your door at noon."

The prisoner figures out that he will not be hanged.

How?

The prisoner correctly reasons that he cannot be hanged on Friday, because if Monday-Thursday pass without him being hanged, a Friday hanging will not be a surprise - therefore, it cannot possibly occur on Friday.

The prisoner then realizes that if he isn't hanged by Wednesday, the hanging cannot occur on Thursday, because, since Friday has been ruled out, Thursday is the only possible day left - therefore, it cannot possibly occur on Thursday, since it won't be a surprise.

The prisoner then realizes that if he isn't hanged by Tuesday, the hanging cannot occur on Wednesday, because, since Thursday has been ruled out, Wednesday is the only possible day left - therefore, it cannot possibly occur on Wednesday, since it won't be a surprise.

The prisoner keeps going backwards, and realizes that all of the days are impossible, and that he will not be hanged the following week.

On Wednesday at noon, the hangman shows up, knocks on the prisoner's door, and the hanging takes place, much to the prisoner's surprise.

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For anyone who has trouble grasping paradoxes, consider the Liar's Paradox: "Everything I say is a lie." 

If they're lying, then it's a true statement; but it can't be a true statement since everything they say is a lie.

Don't think about it too hard - contradictions will mess with your mind.

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On a different subject, if you *really* want to mess with your mind, try and visualize the beginning of time, or the end of space.

Trust me, it's not worth it - it will end up making you dizzy or nauseated (picture a cat trying to understand calculus).

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I don’t remember which teacher or what grade it was in, but I had a teacher tell us this by using a surprise quiz (rather than a hanging) one day next week. For some reason, I remember that above a million other things I was told in school. 

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1 hour ago, dgreen said:

I don’t remember which teacher or what grade it was in, but I had a teacher tell us this by using a surprise quiz (rather than a hanging) one day next week. For some reason, I remember that above a million other things I was told in school. 

This is a variation on the Monty Hall Problem (which Marilyn vos Savant correctly answered). Essentially, odds are pre-determined *at the time of the guess*, and are not affected by someone in-the-know whittling down possibilities *after* the guess.

If the Monty Hall problem is hard to visualize, picture this: You buy a lottery ticket with 1-in-a-million odds of winning. I happen to know what the correct number is, so I remove 999,998 possibilities, leaving only your lottery pick, and one other number. Your odds would still be 1-in-a-million; not 1-in-2. That's obvious, right?

In other words, in that situation, if someone gives you the option to change your lottery number, you'd better damned-well change it!

Interestingly, if I *didn't* know what the correct number was, and somehow successfully removed 999,998 possibilities, your odds of winning - believe it or not - *would* increase to 1-in-2. I can feel the blank stares ...

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