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The New Coffee Room

  1. TNCR
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  3. Puzzle time - prisoners and hats

Puzzle time - prisoners and hats

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  • jon-nycJ Online
    jon-nycJ Online
    jon-nyc
    wrote on last edited by
    #6

    I don't think so. There are a number of 'prisoner hat' problems.

    Only non-witches get due process.

    • Cotton Mather, Salem Massachusetts, 1692
    1 Reply Last reply
    • jon-nycJ jon-nyc

      Possibly, but I think there are a lot of puzzles of this type.

      KlausK Offline
      KlausK Offline
      Klaus
      wrote on last edited by
      #7

      @jon-nyc said in Puzzle time - prisoners and hats:

      Possibly, but I think there are a lot of puzzles of this type.

      Such as these.

      Give me some more time. I know there are many "color of your hat" puzzles, but I'm pretty sure I've also seen one involving probabilities in the past. Maybe not exactly that one.

      1 Reply Last reply
      • KlausK Offline
        KlausK Offline
        Klaus
        wrote on last edited by
        #8

        I think I now remember where I saw the puzzle.

        There's a mathematician who publishes such puzzles on a regular basis, Peter Winkler. He has a monthly column in the "Communications of the ACM", of which I'm a subscriber. I believe I saw that puzzle there. If I think about the puzzle more, I may remember parts of the solution, so I guess I better just keep my mouth shut.

        1 Reply Last reply
        • HoraceH Offline
          HoraceH Offline
          Horace
          wrote on last edited by
          #9

          I guess the set of rules would attempt to clump wrong guesses together while right guesses would tend to be alone. The rules would also want to ensure that at least one person guessed.

          Education is extremely important.

          HoraceH 1 Reply Last reply
          • MikM Away
            MikM Away
            Mik
            wrote on last edited by
            #10

            If they were that smart they wouldn't be prisoners, now would they?

            “I am fond of pigs. Dogs look up to us. Cats look down on us. Pigs treat us as equals.” ~Winston S. Churchill

            1 Reply Last reply
            • HoraceH Offline
              HoraceH Offline
              Horace
              wrote on last edited by
              #11

              Tell that to Stalin and his pogroms against intellectuals.

              Education is extremely important.

              1 Reply Last reply
              • HoraceH Horace

                I guess the set of rules would attempt to clump wrong guesses together while right guesses would tend to be alone. The rules would also want to ensure that at least one person guessed.

                HoraceH Offline
                HoraceH Offline
                Horace
                wrote on last edited by
                #12

                @Horace said in Puzzle time - prisoners and hats:

                I guess the set of rules would attempt to clump wrong guesses together while right guesses would tend to be alone. The rules would also want to ensure that at least one person guessed.

                So, is the answer that simple? Those who see two different colors would not vote. If the other two people are same, guess opposite? This will cause any configuration of colors other than all-same to be a win (one correct vote), while all-same would be a loss (3 wrong votes).

                Education is extremely important.

                1 Reply Last reply
                • KlausK Offline
                  KlausK Offline
                  Klaus
                  wrote on last edited by
                  #13
                  1. Do the prisoners know (or can determine) the order in which they are asked?
                  2. Can the prisoners hear all the answers?
                  1 Reply Last reply
                  • KlausK Offline
                    KlausK Offline
                    Klaus
                    wrote on last edited by
                    #14

                    Oh, I think I now remember the key to the solution. The probability can be raised to 75%.

                    1 Reply Last reply
                    • HoraceH Offline
                      HoraceH Offline
                      Horace
                      wrote on last edited by Horace
                      #15

                      Yes that is the % of my proposed solution. I got there by figuring that each guess would be 50/50 so the rules would have to clump wrong guesses together and single out right ones. One such set of rules leaves 75% of color combinations yielding one right guess.

                      Education is extremely important.

                      1 Reply Last reply
                      • jon-nycJ Online
                        jon-nycJ Online
                        jon-nyc
                        wrote on last edited by
                        #16

                        I got the same answer as Horace.

                        Official answer comes out Saturday but I cant see them improving on 75%.

                        Only non-witches get due process.

                        • Cotton Mather, Salem Massachusetts, 1692
                        1 Reply Last reply
                        • KlausK Offline
                          KlausK Offline
                          Klaus
                          wrote on last edited by
                          #17

                          It gets interesting if you generalize the number of prisoners and/or the number of colors.

                          https://arxiv.org/abs/cs/0509045

                          1 Reply Last reply
                          • jon-nycJ Online
                            jon-nycJ Online
                            jon-nyc
                            wrote on last edited by
                            #18

                            Oh man, you ruined the bonus round. 😉

                            Only non-witches get due process.

                            • Cotton Mather, Salem Massachusetts, 1692
                            1 Reply Last reply
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