Scheduling based problem Unicorn Meta Zoo #1: Why another podcast? Announcing the arrival of Valued Associate #679: Cesar ManaraDeducing Two Numbers based on their Difference and RatioThe 2 million, er, 20 dollar problemAdd a number to each vertex of a triangle such that each edge adds to a perfect squareHexagonal sum fillingEight distinct numbers in the tableIncreasing rows and columnsA simple grid puzzle123456789=1 problemFilling a chessboard with -1, 0 and 1Input/Output Problem #7

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Scheduling based problem



Scheduling based problem



Unicorn Meta Zoo #1: Why another podcast?
Announcing the arrival of Valued Associate #679: Cesar ManaraDeducing Two Numbers based on their Difference and RatioThe 2 million, er, 20 dollar problemAdd a number to each vertex of a triangle such that each edge adds to a perfect squareHexagonal sum fillingEight distinct numbers in the tableIncreasing rows and columnsA simple grid puzzle123456789=1 problemFilling a chessboard with -1, 0 and 1Input/Output Problem #7










4












$begingroup$


Can you place these numbers into 5 rows of 4 such that each row totals 20?




1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8











share|improve this question









$endgroup$
















    4












    $begingroup$


    Can you place these numbers into 5 rows of 4 such that each row totals 20?




    1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8











    share|improve this question









    $endgroup$














      4












      4








      4





      $begingroup$


      Can you place these numbers into 5 rows of 4 such that each row totals 20?




      1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8











      share|improve this question









      $endgroup$




      Can you place these numbers into 5 rows of 4 such that each row totals 20?




      1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 7, 8, 8, 8








      mathematics packing






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 3 hours ago









      JonMark PerryJonMark Perry

      20.9k64199




      20.9k64199




















          3 Answers
          3






          active

          oldest

          votes


















          7












          $begingroup$

          Sure.




          1,5,6,8

          2,4,6,8

          3,4,5,8

          4,4,5,7

          5,5,5,5




          Method:




          Started from the bigger numbers, and partitioned into 5 parts of 20: 8,8,4, 8,7,5 and so on.


          Then swapped a big number with two smaller ones (with the same sum) on another row until I had 4 numbers on each row.




          With some fiddling, it's also possible to get all the columns to add up to 25:




          1,8,6,5

          5,4,7,4

          5,5,5,5

          6,4,2,8

          8,4,5,3




          And here's a magic square (with duplicates, unavoidably) followed by a row of fives:




          1,6,8,5

          5,7,4,4

          8,5,4,3

          6,2,4,8

          5,5,5,5




          And finally:






          4 4 8 4
          8 5 4 3
          1 5 6 8
          7 6 2 5
          5 5 5 5



          This has

          * 20 on all 5 rows

          * 20 on all 4 long diagonals

          * 25 in all 4 columns

          * a magic square on the first 4 rows





          share|improve this answer











          $endgroup$












          • $begingroup$
            I'm late ! But I have differents rows :D
            $endgroup$
            – Narlore
            3 hours ago










          • $begingroup$
            I like the way you went on to challenge yourself by finding solutions to your own proposed questions.
            $endgroup$
            – 5202456
            2 hours ago










          • $begingroup$
            @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-)
            $endgroup$
            – Bass
            59 mins ago


















          2












          $begingroup$

          This one works




          7 3 5 5

          8 2 5 5

          6 4 5 5

          8 6 1 5

          8 4 4 4




          Method :




          Write randomly the numbers on a piece of paper during 5 min until the solution appears magically.







          share|improve this answer











          $endgroup$




















            2












            $begingroup$

            A bit late to the party and cannot beat the excellent answer from @Bass.



            I worked out the number of distinct solutions bearing in mind they can be further permuted by ordering each row and the row sequence. I found




            16 distinct solutions




            I did this by first finding all the sets of four digits which sum to 20.




            There are 17 sets of digits


             1 3 8 8
            1 4 7 8
            1 5 6 8
            1 6 6 7
            2 3 7 8
            2 4 6 8
            2 5 5 8
            2 5 6 7
            3 4 5 8
            3 4 6 7
            3 5 5 7
            3 5 6 6
            4 4 4 8
            4 4 5 7
            4 4 6 6
            4 5 5 6
            5 5 5 5



            I then permuted them for each row so that each digit is used the right number of times.




            These are the 16 solutions


             1 3 8 8 1 3 8 8 1 3 8 8 1 3 8 8
            2 4 6 8 2 5 5 8 2 5 5 8 2 5 6 7
            4 4 5 7 4 4 5 7 4 4 5 7 4 4 4 8
            4 5 5 6 4 4 6 6 4 5 5 6 4 5 5 6
            5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

            1 4 7 8 1 4 7 8 1 4 7 8 1 4 7 8
            2 4 6 8 2 5 5 8 2 5 5 8 2 5 5 8
            3 4 5 8 3 4 5 8 3 4 5 8 3 5 6 6
            4 5 5 6 4 4 6 6 4 5 5 6 4 4 4 8
            5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

            1 5 6 8 1 5 6 8 1 5 6 8 1 5 6 8
            2 3 7 8 2 4 6 8 2 4 6 8 2 5 5 8
            4 4 4 8 3 4 5 8 3 5 5 7 3 4 5 8
            4 5 5 6 4 4 5 7 4 4 4 8 4 4 5 7
            5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 6

            1 5 6 8 1 5 6 8 1 5 6 8 1 6 6 7
            2 5 5 8 2 5 5 8 2 5 6 7 2 5 5 8
            3 4 6 7 3 5 5 7 3 4 5 8 3 4 5 8
            4 4 4 8 4 4 4 8 4 4 4 8 4 4 4 8
            5 5 5 5 4 5 5 6 5 5 5 5 5 5 5 5



            Method:




            A computer program written in C.







            share|improve this answer









            $endgroup$












            • $begingroup$
              Nice! FYI I generated the puzzle from row 2 column 4.
              $endgroup$
              – JonMark Perry
              39 mins ago











            Your Answer








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            3 Answers
            3






            active

            oldest

            votes








            3 Answers
            3






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            7












            $begingroup$

            Sure.




            1,5,6,8

            2,4,6,8

            3,4,5,8

            4,4,5,7

            5,5,5,5




            Method:




            Started from the bigger numbers, and partitioned into 5 parts of 20: 8,8,4, 8,7,5 and so on.


            Then swapped a big number with two smaller ones (with the same sum) on another row until I had 4 numbers on each row.




            With some fiddling, it's also possible to get all the columns to add up to 25:




            1,8,6,5

            5,4,7,4

            5,5,5,5

            6,4,2,8

            8,4,5,3




            And here's a magic square (with duplicates, unavoidably) followed by a row of fives:




            1,6,8,5

            5,7,4,4

            8,5,4,3

            6,2,4,8

            5,5,5,5




            And finally:






            4 4 8 4
            8 5 4 3
            1 5 6 8
            7 6 2 5
            5 5 5 5



            This has

            * 20 on all 5 rows

            * 20 on all 4 long diagonals

            * 25 in all 4 columns

            * a magic square on the first 4 rows





            share|improve this answer











            $endgroup$












            • $begingroup$
              I'm late ! But I have differents rows :D
              $endgroup$
              – Narlore
              3 hours ago










            • $begingroup$
              I like the way you went on to challenge yourself by finding solutions to your own proposed questions.
              $endgroup$
              – 5202456
              2 hours ago










            • $begingroup$
              @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-)
              $endgroup$
              – Bass
              59 mins ago















            7












            $begingroup$

            Sure.




            1,5,6,8

            2,4,6,8

            3,4,5,8

            4,4,5,7

            5,5,5,5




            Method:




            Started from the bigger numbers, and partitioned into 5 parts of 20: 8,8,4, 8,7,5 and so on.


            Then swapped a big number with two smaller ones (with the same sum) on another row until I had 4 numbers on each row.




            With some fiddling, it's also possible to get all the columns to add up to 25:




            1,8,6,5

            5,4,7,4

            5,5,5,5

            6,4,2,8

            8,4,5,3




            And here's a magic square (with duplicates, unavoidably) followed by a row of fives:




            1,6,8,5

            5,7,4,4

            8,5,4,3

            6,2,4,8

            5,5,5,5




            And finally:






            4 4 8 4
            8 5 4 3
            1 5 6 8
            7 6 2 5
            5 5 5 5



            This has

            * 20 on all 5 rows

            * 20 on all 4 long diagonals

            * 25 in all 4 columns

            * a magic square on the first 4 rows





            share|improve this answer











            $endgroup$












            • $begingroup$
              I'm late ! But I have differents rows :D
              $endgroup$
              – Narlore
              3 hours ago










            • $begingroup$
              I like the way you went on to challenge yourself by finding solutions to your own proposed questions.
              $endgroup$
              – 5202456
              2 hours ago










            • $begingroup$
              @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-)
              $endgroup$
              – Bass
              59 mins ago













            7












            7








            7





            $begingroup$

            Sure.




            1,5,6,8

            2,4,6,8

            3,4,5,8

            4,4,5,7

            5,5,5,5




            Method:




            Started from the bigger numbers, and partitioned into 5 parts of 20: 8,8,4, 8,7,5 and so on.


            Then swapped a big number with two smaller ones (with the same sum) on another row until I had 4 numbers on each row.




            With some fiddling, it's also possible to get all the columns to add up to 25:




            1,8,6,5

            5,4,7,4

            5,5,5,5

            6,4,2,8

            8,4,5,3




            And here's a magic square (with duplicates, unavoidably) followed by a row of fives:




            1,6,8,5

            5,7,4,4

            8,5,4,3

            6,2,4,8

            5,5,5,5




            And finally:






            4 4 8 4
            8 5 4 3
            1 5 6 8
            7 6 2 5
            5 5 5 5



            This has

            * 20 on all 5 rows

            * 20 on all 4 long diagonals

            * 25 in all 4 columns

            * a magic square on the first 4 rows





            share|improve this answer











            $endgroup$



            Sure.




            1,5,6,8

            2,4,6,8

            3,4,5,8

            4,4,5,7

            5,5,5,5




            Method:




            Started from the bigger numbers, and partitioned into 5 parts of 20: 8,8,4, 8,7,5 and so on.


            Then swapped a big number with two smaller ones (with the same sum) on another row until I had 4 numbers on each row.




            With some fiddling, it's also possible to get all the columns to add up to 25:




            1,8,6,5

            5,4,7,4

            5,5,5,5

            6,4,2,8

            8,4,5,3




            And here's a magic square (with duplicates, unavoidably) followed by a row of fives:




            1,6,8,5

            5,7,4,4

            8,5,4,3

            6,2,4,8

            5,5,5,5




            And finally:






            4 4 8 4
            8 5 4 3
            1 5 6 8
            7 6 2 5
            5 5 5 5



            This has

            * 20 on all 5 rows

            * 20 on all 4 long diagonals

            * 25 in all 4 columns

            * a magic square on the first 4 rows






            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 1 hour ago

























            answered 3 hours ago









            BassBass

            31.5k474192




            31.5k474192











            • $begingroup$
              I'm late ! But I have differents rows :D
              $endgroup$
              – Narlore
              3 hours ago










            • $begingroup$
              I like the way you went on to challenge yourself by finding solutions to your own proposed questions.
              $endgroup$
              – 5202456
              2 hours ago










            • $begingroup$
              @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-)
              $endgroup$
              – Bass
              59 mins ago
















            • $begingroup$
              I'm late ! But I have differents rows :D
              $endgroup$
              – Narlore
              3 hours ago










            • $begingroup$
              I like the way you went on to challenge yourself by finding solutions to your own proposed questions.
              $endgroup$
              – 5202456
              2 hours ago










            • $begingroup$
              @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-)
              $endgroup$
              – Bass
              59 mins ago















            $begingroup$
            I'm late ! But I have differents rows :D
            $endgroup$
            – Narlore
            3 hours ago




            $begingroup$
            I'm late ! But I have differents rows :D
            $endgroup$
            – Narlore
            3 hours ago












            $begingroup$
            I like the way you went on to challenge yourself by finding solutions to your own proposed questions.
            $endgroup$
            – 5202456
            2 hours ago




            $begingroup$
            I like the way you went on to challenge yourself by finding solutions to your own proposed questions.
            $endgroup$
            – 5202456
            2 hours ago












            $begingroup$
            @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-)
            $endgroup$
            – Bass
            59 mins ago




            $begingroup$
            @5202456 Thanks! The original solution seemed to leave an awful lot of "wiggle room" in the pattern, so I wanted to see what I could do with it. I added one more "extra magical" solution after your comment; hopefully I didn't make any mistakes, as the numbers are starting to bounce around in my eyes :-)
            $endgroup$
            – Bass
            59 mins ago











            2












            $begingroup$

            This one works




            7 3 5 5

            8 2 5 5

            6 4 5 5

            8 6 1 5

            8 4 4 4




            Method :




            Write randomly the numbers on a piece of paper during 5 min until the solution appears magically.







            share|improve this answer











            $endgroup$

















              2












              $begingroup$

              This one works




              7 3 5 5

              8 2 5 5

              6 4 5 5

              8 6 1 5

              8 4 4 4




              Method :




              Write randomly the numbers on a piece of paper during 5 min until the solution appears magically.







              share|improve this answer











              $endgroup$















                2












                2








                2





                $begingroup$

                This one works




                7 3 5 5

                8 2 5 5

                6 4 5 5

                8 6 1 5

                8 4 4 4




                Method :




                Write randomly the numbers on a piece of paper during 5 min until the solution appears magically.







                share|improve this answer











                $endgroup$



                This one works




                7 3 5 5

                8 2 5 5

                6 4 5 5

                8 6 1 5

                8 4 4 4




                Method :




                Write randomly the numbers on a piece of paper during 5 min until the solution appears magically.








                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 3 hours ago

























                answered 3 hours ago









                NarloreNarlore

                35615




                35615





















                    2












                    $begingroup$

                    A bit late to the party and cannot beat the excellent answer from @Bass.



                    I worked out the number of distinct solutions bearing in mind they can be further permuted by ordering each row and the row sequence. I found




                    16 distinct solutions




                    I did this by first finding all the sets of four digits which sum to 20.




                    There are 17 sets of digits


                     1 3 8 8
                    1 4 7 8
                    1 5 6 8
                    1 6 6 7
                    2 3 7 8
                    2 4 6 8
                    2 5 5 8
                    2 5 6 7
                    3 4 5 8
                    3 4 6 7
                    3 5 5 7
                    3 5 6 6
                    4 4 4 8
                    4 4 5 7
                    4 4 6 6
                    4 5 5 6
                    5 5 5 5



                    I then permuted them for each row so that each digit is used the right number of times.




                    These are the 16 solutions


                     1 3 8 8 1 3 8 8 1 3 8 8 1 3 8 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 6 7
                    4 4 5 7 4 4 5 7 4 4 5 7 4 4 4 8
                    4 5 5 6 4 4 6 6 4 5 5 6 4 5 5 6
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 4 7 8 1 4 7 8 1 4 7 8 1 4 7 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 5 8
                    3 4 5 8 3 4 5 8 3 4 5 8 3 5 6 6
                    4 5 5 6 4 4 6 6 4 5 5 6 4 4 4 8
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 5 6 8 1 5 6 8 1 5 6 8 1 5 6 8
                    2 3 7 8 2 4 6 8 2 4 6 8 2 5 5 8
                    4 4 4 8 3 4 5 8 3 5 5 7 3 4 5 8
                    4 5 5 6 4 4 5 7 4 4 4 8 4 4 5 7
                    5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 6

                    1 5 6 8 1 5 6 8 1 5 6 8 1 6 6 7
                    2 5 5 8 2 5 5 8 2 5 6 7 2 5 5 8
                    3 4 6 7 3 5 5 7 3 4 5 8 3 4 5 8
                    4 4 4 8 4 4 4 8 4 4 4 8 4 4 4 8
                    5 5 5 5 4 5 5 6 5 5 5 5 5 5 5 5



                    Method:




                    A computer program written in C.







                    share|improve this answer









                    $endgroup$












                    • $begingroup$
                      Nice! FYI I generated the puzzle from row 2 column 4.
                      $endgroup$
                      – JonMark Perry
                      39 mins ago















                    2












                    $begingroup$

                    A bit late to the party and cannot beat the excellent answer from @Bass.



                    I worked out the number of distinct solutions bearing in mind they can be further permuted by ordering each row and the row sequence. I found




                    16 distinct solutions




                    I did this by first finding all the sets of four digits which sum to 20.




                    There are 17 sets of digits


                     1 3 8 8
                    1 4 7 8
                    1 5 6 8
                    1 6 6 7
                    2 3 7 8
                    2 4 6 8
                    2 5 5 8
                    2 5 6 7
                    3 4 5 8
                    3 4 6 7
                    3 5 5 7
                    3 5 6 6
                    4 4 4 8
                    4 4 5 7
                    4 4 6 6
                    4 5 5 6
                    5 5 5 5



                    I then permuted them for each row so that each digit is used the right number of times.




                    These are the 16 solutions


                     1 3 8 8 1 3 8 8 1 3 8 8 1 3 8 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 6 7
                    4 4 5 7 4 4 5 7 4 4 5 7 4 4 4 8
                    4 5 5 6 4 4 6 6 4 5 5 6 4 5 5 6
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 4 7 8 1 4 7 8 1 4 7 8 1 4 7 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 5 8
                    3 4 5 8 3 4 5 8 3 4 5 8 3 5 6 6
                    4 5 5 6 4 4 6 6 4 5 5 6 4 4 4 8
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 5 6 8 1 5 6 8 1 5 6 8 1 5 6 8
                    2 3 7 8 2 4 6 8 2 4 6 8 2 5 5 8
                    4 4 4 8 3 4 5 8 3 5 5 7 3 4 5 8
                    4 5 5 6 4 4 5 7 4 4 4 8 4 4 5 7
                    5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 6

                    1 5 6 8 1 5 6 8 1 5 6 8 1 6 6 7
                    2 5 5 8 2 5 5 8 2 5 6 7 2 5 5 8
                    3 4 6 7 3 5 5 7 3 4 5 8 3 4 5 8
                    4 4 4 8 4 4 4 8 4 4 4 8 4 4 4 8
                    5 5 5 5 4 5 5 6 5 5 5 5 5 5 5 5



                    Method:




                    A computer program written in C.







                    share|improve this answer









                    $endgroup$












                    • $begingroup$
                      Nice! FYI I generated the puzzle from row 2 column 4.
                      $endgroup$
                      – JonMark Perry
                      39 mins ago













                    2












                    2








                    2





                    $begingroup$

                    A bit late to the party and cannot beat the excellent answer from @Bass.



                    I worked out the number of distinct solutions bearing in mind they can be further permuted by ordering each row and the row sequence. I found




                    16 distinct solutions




                    I did this by first finding all the sets of four digits which sum to 20.




                    There are 17 sets of digits


                     1 3 8 8
                    1 4 7 8
                    1 5 6 8
                    1 6 6 7
                    2 3 7 8
                    2 4 6 8
                    2 5 5 8
                    2 5 6 7
                    3 4 5 8
                    3 4 6 7
                    3 5 5 7
                    3 5 6 6
                    4 4 4 8
                    4 4 5 7
                    4 4 6 6
                    4 5 5 6
                    5 5 5 5



                    I then permuted them for each row so that each digit is used the right number of times.




                    These are the 16 solutions


                     1 3 8 8 1 3 8 8 1 3 8 8 1 3 8 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 6 7
                    4 4 5 7 4 4 5 7 4 4 5 7 4 4 4 8
                    4 5 5 6 4 4 6 6 4 5 5 6 4 5 5 6
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 4 7 8 1 4 7 8 1 4 7 8 1 4 7 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 5 8
                    3 4 5 8 3 4 5 8 3 4 5 8 3 5 6 6
                    4 5 5 6 4 4 6 6 4 5 5 6 4 4 4 8
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 5 6 8 1 5 6 8 1 5 6 8 1 5 6 8
                    2 3 7 8 2 4 6 8 2 4 6 8 2 5 5 8
                    4 4 4 8 3 4 5 8 3 5 5 7 3 4 5 8
                    4 5 5 6 4 4 5 7 4 4 4 8 4 4 5 7
                    5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 6

                    1 5 6 8 1 5 6 8 1 5 6 8 1 6 6 7
                    2 5 5 8 2 5 5 8 2 5 6 7 2 5 5 8
                    3 4 6 7 3 5 5 7 3 4 5 8 3 4 5 8
                    4 4 4 8 4 4 4 8 4 4 4 8 4 4 4 8
                    5 5 5 5 4 5 5 6 5 5 5 5 5 5 5 5



                    Method:




                    A computer program written in C.







                    share|improve this answer









                    $endgroup$



                    A bit late to the party and cannot beat the excellent answer from @Bass.



                    I worked out the number of distinct solutions bearing in mind they can be further permuted by ordering each row and the row sequence. I found




                    16 distinct solutions




                    I did this by first finding all the sets of four digits which sum to 20.




                    There are 17 sets of digits


                     1 3 8 8
                    1 4 7 8
                    1 5 6 8
                    1 6 6 7
                    2 3 7 8
                    2 4 6 8
                    2 5 5 8
                    2 5 6 7
                    3 4 5 8
                    3 4 6 7
                    3 5 5 7
                    3 5 6 6
                    4 4 4 8
                    4 4 5 7
                    4 4 6 6
                    4 5 5 6
                    5 5 5 5



                    I then permuted them for each row so that each digit is used the right number of times.




                    These are the 16 solutions


                     1 3 8 8 1 3 8 8 1 3 8 8 1 3 8 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 6 7
                    4 4 5 7 4 4 5 7 4 4 5 7 4 4 4 8
                    4 5 5 6 4 4 6 6 4 5 5 6 4 5 5 6
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 4 7 8 1 4 7 8 1 4 7 8 1 4 7 8
                    2 4 6 8 2 5 5 8 2 5 5 8 2 5 5 8
                    3 4 5 8 3 4 5 8 3 4 5 8 3 5 6 6
                    4 5 5 6 4 4 6 6 4 5 5 6 4 4 4 8
                    5 5 5 5 5 5 5 5 4 5 5 6 5 5 5 5

                    1 5 6 8 1 5 6 8 1 5 6 8 1 5 6 8
                    2 3 7 8 2 4 6 8 2 4 6 8 2 5 5 8
                    4 4 4 8 3 4 5 8 3 5 5 7 3 4 5 8
                    4 5 5 6 4 4 5 7 4 4 4 8 4 4 5 7
                    5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 6

                    1 5 6 8 1 5 6 8 1 5 6 8 1 6 6 7
                    2 5 5 8 2 5 5 8 2 5 6 7 2 5 5 8
                    3 4 6 7 3 5 5 7 3 4 5 8 3 4 5 8
                    4 4 4 8 4 4 4 8 4 4 4 8 4 4 4 8
                    5 5 5 5 4 5 5 6 5 5 5 5 5 5 5 5



                    Method:




                    A computer program written in C.








                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 48 mins ago









                    Weather VaneWeather Vane

                    2,623114




                    2,623114











                    • $begingroup$
                      Nice! FYI I generated the puzzle from row 2 column 4.
                      $endgroup$
                      – JonMark Perry
                      39 mins ago
















                    • $begingroup$
                      Nice! FYI I generated the puzzle from row 2 column 4.
                      $endgroup$
                      – JonMark Perry
                      39 mins ago















                    $begingroup$
                    Nice! FYI I generated the puzzle from row 2 column 4.
                    $endgroup$
                    – JonMark Perry
                    39 mins ago




                    $begingroup$
                    Nice! FYI I generated the puzzle from row 2 column 4.
                    $endgroup$
                    – JonMark Perry
                    39 mins ago

















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