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One-digit products in a row of numbers


Can you fill a 3x3 grid with these numbers so the products of the rows and columns are the same?Increasing rows and columnsWhat is my four digit car number?Four-by-four table with equal row and column products90s Number PuzzleIn a square, arrange the binary numbers such that no $n$:th digit is the same along a row or columnThree-digit multiplication puzzle, part III: Return of the HexHow do I make numbers 50-100 using only the numbers 2, 0, 1, 9?Squares inside a square






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








8












$begingroup$


The digits from 1 to 9 can be arranged in a row, such that any two
neighbouring digits in this row is the product of two one-digit numbers.
Arrangement:




$$728163549$$




Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
Example: 123456789ABCDEF
12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.










share|improve this question











$endgroup$




















    8












    $begingroup$


    The digits from 1 to 9 can be arranged in a row, such that any two
    neighbouring digits in this row is the product of two one-digit numbers.
    Arrangement:




    $$728163549$$




    Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
    Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
    Example: 123456789ABCDEF
    12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.










    share|improve this question











    $endgroup$
















      8












      8








      8


      1



      $begingroup$


      The digits from 1 to 9 can be arranged in a row, such that any two
      neighbouring digits in this row is the product of two one-digit numbers.
      Arrangement:




      $$728163549$$




      Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
      Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
      Example: 123456789ABCDEF
      12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.










      share|improve this question











      $endgroup$




      The digits from 1 to 9 can be arranged in a row, such that any two
      neighbouring digits in this row is the product of two one-digit numbers.
      Arrangement:




      $$728163549$$




      Is it possible to do such an arrangement using hexadecimal digits 1-9 and A-F?
      Here the row has 15 digits and all numbers are treated as hexadecimal numbers.
      Example: 123456789ABCDEF
      12=2*9, 23=5*7, 34=4*D, 45 does not work, etc.







      mathematics calculation-puzzle






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 10 hours ago









      JMP

      25.8k6 gold badges49 silver badges111 bronze badges




      25.8k6 gold badges49 silver badges111 bronze badges










      asked 10 hours ago









      ThomasLThomasL

      7902 silver badges19 bronze badges




      7902 silver badges19 bronze badges























          2 Answers
          2






          active

          oldest

          votes


















          6














          $begingroup$

          One solution is




          $$D2379A5B6C4E18F$$
          enter image description here




          Thought process:




          No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.

          The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$

          Therefore we must have subsequences $E1$ and $D2$.

          From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$







          share|improve this answer











          $endgroup$






















            2














            $begingroup$

            As an addendum to the answer from @Arnaud:




            The smallest such number is 375B6E19C4D2A8F.
            According to the brute-force program I made, there are just $787$ solutions.







            share|improve this answer











            $endgroup$

















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              2 Answers
              2






              active

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              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              6














              $begingroup$

              One solution is




              $$D2379A5B6C4E18F$$
              enter image description here




              Thought process:




              No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.

              The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$

              Therefore we must have subsequences $E1$ and $D2$.

              From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$







              share|improve this answer











              $endgroup$



















                6














                $begingroup$

                One solution is




                $$D2379A5B6C4E18F$$
                enter image description here




                Thought process:




                No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.

                The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$

                Therefore we must have subsequences $E1$ and $D2$.

                From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$







                share|improve this answer











                $endgroup$

















                  6














                  6










                  6







                  $begingroup$

                  One solution is




                  $$D2379A5B6C4E18F$$
                  enter image description here




                  Thought process:




                  No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.

                  The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$

                  Therefore we must have subsequences $E1$ and $D2$.

                  From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$







                  share|improve this answer











                  $endgroup$



                  One solution is




                  $$D2379A5B6C4E18F$$
                  enter image description here




                  Thought process:




                  No product starts with $F$, so $F$ must be at the end, and the only options are $3F$ and $8F$.

                  The only $2$-digit numbers that are products of $1$-digit number and start with digits $A, B, C, D, E$ are $$A5, A8, A9, B4, B6, C3, C4, D2, E1.$$

                  Therefore we must have subsequences $E1$ and $D2$.

                  From this, you quickly get an answer by looking at the above table. I don't know if I was lucky, but apart from the observations above, I guessed all the rest right. Just for the sake of it, here is another one: $$D24E1879A5B6C3F$$








                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited 8 hours ago

























                  answered 9 hours ago









                  Arnaud MortierArnaud Mortier

                  5,77413 silver badges49 bronze badges




                  5,77413 silver badges49 bronze badges


























                      2














                      $begingroup$

                      As an addendum to the answer from @Arnaud:




                      The smallest such number is 375B6E19C4D2A8F.
                      According to the brute-force program I made, there are just $787$ solutions.







                      share|improve this answer











                      $endgroup$



















                        2














                        $begingroup$

                        As an addendum to the answer from @Arnaud:




                        The smallest such number is 375B6E19C4D2A8F.
                        According to the brute-force program I made, there are just $787$ solutions.







                        share|improve this answer











                        $endgroup$

















                          2














                          2










                          2







                          $begingroup$

                          As an addendum to the answer from @Arnaud:




                          The smallest such number is 375B6E19C4D2A8F.
                          According to the brute-force program I made, there are just $787$ solutions.







                          share|improve this answer











                          $endgroup$



                          As an addendum to the answer from @Arnaud:




                          The smallest such number is 375B6E19C4D2A8F.
                          According to the brute-force program I made, there are just $787$ solutions.








                          share|improve this answer














                          share|improve this answer



                          share|improve this answer








                          edited 8 hours ago

























                          answered 8 hours ago









                          JensJens

                          3966 bronze badges




                          3966 bronze badges































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