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The New Coffee Room

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  3. Puzzle Time - Marks on the Die

Puzzle Time - Marks on the Die

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  • J Offline
    J Offline
    jon-nyc
    wrote on 18 Jul 2022, 15:48 last edited by
    #1

    I have an unlabeled, six-sided die. I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

    How many unique ways are there for me to mark the die? (Note: If two ways can be rotated so that they appear the same, then they are considered to be the same marking.)

    Extra credit: Suppose you can also mark a face along one of its two diagonals. Now how many unique ways are there to mark the die?

    Thank you for your attention to this matter.

    K 1 Reply Last reply 18 Jul 2022, 17:09
    • J jon-nyc
      18 Jul 2022, 15:48

      I have an unlabeled, six-sided die. I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

      How many unique ways are there for me to mark the die? (Note: If two ways can be rotated so that they appear the same, then they are considered to be the same marking.)

      Extra credit: Suppose you can also mark a face along one of its two diagonals. Now how many unique ways are there to mark the die?

      K Offline
      K Offline
      Klaus
      wrote on 18 Jul 2022, 17:09 last edited by
      #2

      @jon-nyc said in Puzzle Time - Marks on the Die:

      I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

      I don't quite understand. What is a mark? A dot? What does "parallel" mean when we are not talking about lines or planes?

      T 1 Reply Last reply 19 Jul 2022, 02:00
      • K Klaus
        18 Jul 2022, 17:09

        @jon-nyc said in Puzzle Time - Marks on the Die:

        I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

        I don't quite understand. What is a mark? A dot? What does "parallel" mean when we are not talking about lines or planes?

        T Offline
        T Offline
        taiwan_girl
        wrote on 19 Jul 2022, 02:00 last edited by
        #3

        @Klaus said in Puzzle Time - Marks on the Die:

        @jon-nyc said in Puzzle Time - Marks on the Die:

        I make a single mark on the middle of each face that is parallel to one pair of that face’s four edges.

        I don't quite understand. What is a mark? A dot? What does "parallel" mean when we are not talking about lines or planes?

        My question also. How can a dot be parallel to something?

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        • J Offline
          J Offline
          jon-nyc
          wrote on 19 Jul 2022, 18:08 last edited by
          #4

          Questionology 101 tells me this is a problem about symmetry and rotation.

          So clearly imagine a mark that is not a dot, rather a short line segment in the center of the die face, and drawn parallel to one side or another.

          Clearly we would assume that all marks made are identical in length and placement on the face relative to the center, so that we wouldn’t distinguish one set of markings vs another on such factors.

          Thank you for your attention to this matter.

          1 Reply Last reply
          • K Offline
            K Offline
            Klaus
            wrote on 19 Jul 2022, 18:36 last edited by
            #5

            So you are saying there are only two possible marks for each face? So the answer is 2^6 minus the ones that are the same by rotation?

            A 1 Reply Last reply 20 Jul 2022, 14:50
            • J Offline
              J Offline
              jon-nyc
              wrote on 20 Jul 2022, 14:35 last edited by jon-nyc
              #6

              That’s my read. Otherwise the question becomes “how many distinct marks can you draw” or “how many distinct spots on a face can you put a mark” which seems unlikely for a puzzle.

              Thank you for your attention to this matter.

              1 Reply Last reply
              • K Klaus
                19 Jul 2022, 18:36

                So you are saying there are only two possible marks for each face? So the answer is 2^6 minus the ones that are the same by rotation?

                A Away
                A Away
                Axtremus
                wrote on 20 Jul 2022, 14:50 last edited by
                #7

                @Klaus said in Puzzle Time - Marks on the Die:

                … the ones that are the same by rotation?

                Figuring out “the ones that are the same by rotation” is challenging. :man-shrugging:

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                19 Jul 2022, 18:08


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