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Author Topic: An unexpected execution  (Read 3387 times)

« on: November 14, 2010, 04:03:28 AM »
Hey guys let's play a game.

A judge tells a condemned prisoner that he will be hanged at noon on one weekday during 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:

1. 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; therefore, 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.

2. 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.

Where did the prisoner's logic go wrong?
Luigison: Question everything!
Me: Why?

WarpRattler

  • Paid by the word
« Reply #1 on: November 14, 2010, 11:14:49 AM »
His reasoning relied solely on the premise that if he was not hanged one day, it would have to be the next day and therefore not be a surprise, when in reality it meant it could be any remaining day that week; the only situation where it would not be a surprise would be his initial conclusion, that if he was not hanged by Thursday it had to be Friday.

CrossEyed7

  • i can make this whatever i want; you're not my dad
« Reply #2 on: November 14, 2010, 12:50:45 PM »
By convincing himself that the execution could never occur, he then ensured that any execution would be a surprise. He failed to factor his own reasoning into his reasoning.
"Oh man, I wish being a part of a Mario fan community was the most embarrassing thing about my life." - Super-Jesse

Black Mage

  • HP 1018 MP 685
« Reply #3 on: November 14, 2010, 07:16:44 PM »
By convincing himself that the execution could never occur, he then ensured that any execution would be a surprise. He failed to factor his own reasoning into his reasoning.

That was my thought immediately after reading it, yes.

« Reply #4 on: November 14, 2010, 08:11:55 PM »
I immediately came to Warp's conclusion, but didn't think about CrossEyed's, that was pretty cool.

CrossEyed7

  • i can make this whatever i want; you're not my dad
« Reply #5 on: November 14, 2010, 08:39:35 PM »
Imagine the look on the guy's face when the executioner comes in.

"What? You can't be here! I'm not surpri... ooooohhhhh."
"Oh man, I wish being a part of a Mario fan community was the most embarrassing thing about my life." - Super-Jesse

« Reply #6 on: November 15, 2010, 03:32:14 AM »
Very good you guys. I like Warp's resolution the best but CrossEyed's is definitely valid. How about another one?

"This statement is false." Assign a truth value to this statement.
Luigison: Question everything!
Me: Why?

WarpRattler

  • Paid by the word
« Reply #7 on: November 15, 2010, 09:00:59 AM »
NaN

« Reply #8 on: November 15, 2010, 10:30:40 AM »
PL's statement is true because it is stating that it is false, which in turn makes it true.

Kinda reminds me of the two doors from.. the movie Labyrinth, I think. One door only tells the truth, the other one only lies. Both are blocking a path further into the maze and to get them to open, Sarah had to talk to them and figure out which door was which. I actually sorta forget what the solution is.. I find it confusing.
Kinopio is the ultimate video game character! Who else can drive a kart, host parties, play tennis, give good advice and items, and is almost always happy??

WarpRattler

  • Paid by the word
« Reply #9 on: November 15, 2010, 10:40:17 AM »
For the record, it's the liar's paradox.

« Reply #10 on: November 15, 2010, 03:01:30 PM »
Warp is correct.

Anyone else have something to share?
Luigison: Question everything!
Me: Why?

« Reply #11 on: November 15, 2010, 03:31:11 PM »
Technically, it's got an element of truth in that the statement is not true, but it's also not false.
If she is indeed genetically mutated such that she has an eye in the back of her head, then I guess that she is genetically mutated and has an eye in the back of her head.

Luigison

  • Old Person™
« Reply #12 on: November 15, 2010, 06:48:49 PM »
Here's an easy one:

How can you throw a ball as hard as you can and have it come back to you, even if it doesn't bounce off anything? There is nothing attached to it, and no one else catches or throws it back to you.

For a harder one lookup the "problem of evil."  Feel free to post about it, but not at the dinner table, or in this case, the game table. 
“Evolution has shaped us with perceptions that allow us to survive. But part of that involves hiding from us the stuff we don’t need to know."

CrossEyed7

  • i can make this whatever i want; you're not my dad
« Reply #13 on: November 15, 2010, 07:29:29 PM »
I'm assuming the real answer is throw it straight up, but that's boring and it'd be more fun to say throw it all the way around the world.
"Oh man, I wish being a part of a Mario fan community was the most embarrassing thing about my life." - Super-Jesse

« Reply #14 on: November 15, 2010, 08:06:27 PM »
Luigison, just toss it upwards!

EDIT: Ah, CrossEyed had the same answer.
« Last Edit: November 15, 2010, 08:09:36 PM by PaperLuigi »
Luigison: Question everything!
Me: Why?

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