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The New Coffee Room

  1. TNCR
  2. General Discussion
  3. Puzzle Time

Puzzle Time

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  • jon-nycJ jon-nyc

    How would you do the encoding of the 48? What kind of prima facie coding scheme would you use when you don’t know in advance which 48 cards you’ll be distinguishing among?

    Ax - you’re on the right track. Or a right track at least.

    KlausK Offline
    KlausK Offline
    Klaus
    wrote on last edited by Klaus
    #16

    @jon-nyc said in Puzzle Time:

    What kind of prima facie coding scheme would you use when you don’t know in advance which 48 cards you’ll be distinguishing among?

    That part's easy.

    From the 52 cards, subtract the 4 cards that were handed to Cats. Sort them. Name them 1 to 48.

    The number encoding is: Name the 24 sorting orders s1 to s24. If you transmit 0 via the method I described above, sorting s-n stands for card n. If you transmit 1, it stands for 24+n.

    1 Reply Last reply
    • jon-nycJ Offline
      jon-nycJ Offline
      jon-nyc
      wrote on last edited by
      #17

      Right but the need to choose a particular card to implement your ‘bit’ could conflict with your ability to represent the number, couldn't it?

      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
        #18

        Yes, but I was kind of hoping you wouldn't notice.

        1 Reply Last reply
        • jon-nycJ Offline
          jon-nycJ Offline
          jon-nyc
          wrote on last edited by
          #19

          Lol.

          There’s a much easier way which people could easily do in their head in real time to make the trick work.

          Only non-witches get due process.

          • Cotton Mather, Salem Massachusetts, 1692
          1 Reply Last reply
          • HoraceH Offline
            HoraceH Offline
            Horace
            wrote on last edited by Horace
            #20

            :::

            Considering 5 random distinct numbers from 1 to 52, the magician could choose either the highest or the lowest number to keep secret, while ordering the remaining four to identify a number between 1 and 24, since there are 24 orderings of four distinct things A,B,C, and D where A is the lowest number, B the second lowest, etc. The magician would choose either the highest or lowest of the 5 numbers, whichever one was within 24 of the remaining highest number, considering 52 to roll over to 1 as numbers increase. This should always be possible. The assistant would identify the hidden number as the indicated offset from the highest of their four cards, rolling over from 52 to 1 if necessary.

            :::

            Education is extremely important.

            KlausK 1 Reply Last reply
            • jon-nycJ Offline
              jon-nycJ Offline
              jon-nyc
              wrote on last edited by jon-nyc
              #21

              :::

              Yes that should work.

              A conceptually similar solution that is easier to compute in your head in ‘magic trick time’:

              Based in Ax’s observation that there is always at least one suit with two cards within the 5.

              George chooses one of the two cards of the same suit, puts the other on top of the four he hands to Cats.

              With the other three cards he can communicate a number between 1-6. He use that number to indicate how much higher the reserved card is than the top card, allowing for the cycle from K->A->2.

              Example. He puts the queen of clubs on top with the reserved card being the 5. He indicates 6 with the other three cards. Cats knows that from Q you count K,A,2,3,4,5 so the reserved card is a 5.

              What if the reserved card was a six? In that case George would have reserved the Q and handed Cats the 6 on top of the deck, still indicating 6 with the other three cards. (7,8,9,10,J,Q). In other words, by strategically choosing between the two cards of that suit, the additional 3 cards can convey enough information.

              :::

              Only non-witches get due process.

              • Cotton Mather, Salem Massachusetts, 1692
              1 Reply Last reply
              • HoraceH Offline
                HoraceH Offline
                Horace
                wrote on last edited by Horace
                #22

                Yeah that's conceptually identical but for the range being 1-13 rather than 1-52. But with some practice I don't think either is particularly difficult to compute in magic trick time. To identify the number between 0 and 23 based on the order of 4 cards, let hte first card indicate which quartile the number is in, then the second card indicate which tri-cile of that, and the third card which of the two remaining numbers it is.

                Education is extremely important.

                1 Reply Last reply
                • HoraceH Horace

                  :::

                  Considering 5 random distinct numbers from 1 to 52, the magician could choose either the highest or the lowest number to keep secret, while ordering the remaining four to identify a number between 1 and 24, since there are 24 orderings of four distinct things A,B,C, and D where A is the lowest number, B the second lowest, etc. The magician would choose either the highest or lowest of the 5 numbers, whichever one was within 24 of the remaining highest number, considering 52 to roll over to 1 as numbers increase. This should always be possible. The assistant would identify the hidden number as the indicated offset from the highest of their four cards, rolling over from 52 to 1 if necessary.

                  :::

                  KlausK Offline
                  KlausK Offline
                  Klaus
                  wrote on last edited by
                  #23

                  @Horace said in Puzzle Time:

                  The magician would choose either the highest or lowest of the 5 numbers, whichever one was within 24 of the remaining highest number

                  Ah yes, that was the puzzle piece I was missing.

                  1 Reply Last reply
                  • HoraceH Offline
                    HoraceH Offline
                    Horace
                    wrote on last edited by
                    #24

                    jon where do you get these puzzles? Or do you invent them?

                    Education is extremely important.

                    1 Reply Last reply
                    • jon-nycJ Offline
                      jon-nycJ Offline
                      jon-nyc
                      wrote on last edited by
                      #25

                      Mostly from a mailing list from a university ‘math circle‘ we were involved with in NC

                      Only non-witches get due process.

                      • Cotton Mather, Salem Massachusetts, 1692
                      1 Reply Last reply
                      • HoraceH Offline
                        HoraceH Offline
                        Horace
                        wrote on last edited by
                        #26

                        Today it is my responsibility to present a game during a department zoom meeting that we can all participate in. I'm going to give them this puzzle, but I'll have them try to solve it as a group rather than individually and competitively. Should be fun. Maybe I'll be surprised and they'll come up with a solution quickly.

                        Education is extremely important.

                        jon-nycJ 1 Reply Last reply
                        • jon-nycJ Offline
                          jon-nycJ Offline
                          jon-nyc
                          wrote on last edited by
                          #27

                          Cool. make sure you say 'copyright jon-nyc 2020'.

                          Only non-witches get due process.

                          • Cotton Mather, Salem Massachusetts, 1692
                          1 Reply Last reply
                          • jon-nycJ Offline
                            jon-nycJ Offline
                            jon-nyc
                            wrote on last edited by jon-nyc
                            #28

                            I've since learned that this very method (using top card as suit indicator and three cards as identifier) was used by a magician from the 30s. Probably invented by him.

                            Only non-witches get due process.

                            • Cotton Mather, Salem Massachusetts, 1692
                            HoraceH 1 Reply Last reply
                            • jon-nycJ Offline
                              jon-nycJ Offline
                              jon-nyc
                              wrote on last edited by jon-nyc
                              #29

                              William Fitch Cheney, was his name. Apparently a mathematician and magician.

                              Only non-witches get due process.

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

                                I've since learned that this very method (using top card as suit indicator and three cards as identifier) was used by a magician from the 30s. Probably invented by him.

                                HoraceH Offline
                                HoraceH Offline
                                Horace
                                wrote on last edited by
                                #30

                                @jon-nyc said in Puzzle Time:

                                I've since learned that this very method (using top card as suit indicator and three cards as identifier) was used by a magician from the 30s. Probably invented by him.

                                It's a garbage method compared to mine.

                                Education is extremely important.

                                1 Reply Last reply
                                • HoraceH Horace

                                  Today it is my responsibility to present a game during a department zoom meeting that we can all participate in. I'm going to give them this puzzle, but I'll have them try to solve it as a group rather than individually and competitively. Should be fun. Maybe I'll be surprised and they'll come up with a solution quickly.

                                  jon-nycJ Offline
                                  jon-nycJ Offline
                                  jon-nyc
                                  wrote on last edited by
                                  #31

                                  @Horace said in Puzzle Time:

                                  Today it is my responsibility to present a game during a department zoom meeting that we can all participate in. I'm going to give them this puzzle, but I'll have them try to solve it as a group rather than individually and competitively. Should be fun. Maybe I'll be surprised and they'll come up with a solution quickly.

                                  How'd it go?

                                  Only non-witches get due process.

                                  • Cotton Mather, Salem Massachusetts, 1692
                                  1 Reply Last reply
                                  • HoraceH Offline
                                    HoraceH Offline
                                    Horace
                                    wrote on last edited by
                                    #32

                                    There was a surprise guest and thus no game-time during that meeting. Then the following week there was again no game time. I suppose I'll be on the hook but only if we ever do another game time. Nobody likes these game times during these meetings, but games are fun, and even if nobody has any fun, they are still fun. Just ask everybody professionally obligated to attend the zoom meeting.

                                    Education is extremely important.

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