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  • #1

    Math Puzzle Thread

    I heard a neat one recently.

    There are N people in a dungeon. The dungeon master has a a bunch of colored hats, with an arbitrary distribution among N distinct colors (they could all be blue, there could be one of each, etc.). He tells them that he's going to distribute the hats to everyone, and at least one person has to guess his or her hat correctly or else everyone dies. He allows them to meet and discuss some sort of algorithm to figure out how to do this in advance. After he distributes the hats, they aren't allowed to communicate, signal, etc. in any way. All they can do is see the color of everyone else's hat.

    So what strategy should they take? You can suppose that everyone has a really good memory.
    "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
    -Bokonon
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  • #2
    Are you sure they can't signal in any way? Not even to say "I haven't figured it out yet"?

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    • #3
      each should look at everyone else's hat. and if everyone's is one color they should assume that theirs is that color as well. or they should all guess blue.

      or since they are in a dungeon they could look for puddles to see their hat's color in.

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      • #4

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        • #5
          You can, but then the dungeon master'll kill you and everyone else.
          "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
          -Bokonon

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          • #6
            Bastard

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            • #7

              i shall ponder this...
              Order of the Fly
              Those that cannot curse, cannot heal.

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              • #8
                Wait, but you can guess and get it wrong but not die until everyone has guessed?

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                • #9
                  Can everyone else hear your guess? Can they tell whether or not you've submitted a guess?

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                  • #10
                    Nope.
                    "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
                    -Bokonon

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                    • #11
                      To which of those questions?

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                      • #12
                        The first prisoner looks at the second prisoner's hat and "guesses" that colour, then the second prisoner proceeds to set them all free.

                        edit: quite an x-post
                        THEY!!111 OMG WTF LOL LET DA NOMADS AND TEH S3D3NTARY PEOPLA BOTH MAEK BITER AXP3REINCES
                        AND TEH GRAAT SINS OF THERE [DOCTRINAL] INOVATIONS BQU3ATH3D SMAL
                        AND!!1!11!!! LOL JUST IN CAES A DISPUTANT CALS U 2 DISPUT3 ABOUT THEYRE CLAMES
                        DO NOT THAN DISPUT3 ON THEM 3XCAPT BY WAY OF AN 3XTARNAL DISPUTA!!!!11!! WTF

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                        • #13
                          Originally posted by LordShiva
                          The first prisoner looks at the second prisoner's hat and "guesses" that colour, then the second prisoner proceeds to set them all free.
                          That's too easy, which is why I asked if they can hear the other guess.

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                          • #14
                            To which of those questions?
                            Your second set. No communication means no communication.
                            "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
                            -Bokonon

                            Comment

                            • #15
                              thats the answer?
                              Order of the Fly
                              Those that cannot curse, cannot heal.

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