How to solve with each variable having an unique value?

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I have a puzzle for example:




Use 1 to 9, once only in the cells so that you obtain row and column products as shown:
enter image description here




mypuzzle2[val1_, val2_, val3_, val4_, val5_, val6_] := Solve[a*b*c == val1, d*e*f == val2, g*h*i == val3, a*d*g == val4, b*e*h == val5, c*f*i == val6, a > 0, b > 0, c > 0, d > 0, e > 0, f > 0, g > 0, h > 0, i > 0, a < 10, b < 10, c < 10, d < 10, e < 10, f < 10, g < 10, h < 10, i < 10, a, b, c, d, e, f, g, h, i, Integers]


mypuzzle2[80, 63, 72, 72, 48, 105]


enter image description here



How do I modify the code, so that it only returns with the answer with unique values of 1 to 9?



Thanks.






equation-solving







share|improve this question

























    up vote
    4
    down vote

    favorite












    I have a puzzle for example:




    Use 1 to 9, once only in the cells so that you obtain row and column products as shown:
    enter image description here




    mypuzzle2[val1_, val2_, val3_, val4_, val5_, val6_] := Solve[a*b*c == val1, d*e*f == val2, g*h*i == val3, a*d*g == val4, b*e*h == val5, c*f*i == val6, a > 0, b > 0, c > 0, d > 0, e > 0, f > 0, g > 0, h > 0, i > 0, a < 10, b < 10, c < 10, d < 10, e < 10, f < 10, g < 10, h < 10, i < 10, a, b, c, d, e, f, g, h, i, Integers]


    mypuzzle2[80, 63, 72, 72, 48, 105]


    enter image description here



    How do I modify the code, so that it only returns with the answer with unique values of 1 to 9?



    Thanks.






    equation-solving







    share|improve this question























      up vote
      4
      down vote

      favorite









      up vote
      4
      down vote

      favorite











      I have a puzzle for example:




      Use 1 to 9, once only in the cells so that you obtain row and column products as shown:
      enter image description here




      mypuzzle2[val1_, val2_, val3_, val4_, val5_, val6_] := Solve[a*b*c == val1, d*e*f == val2, g*h*i == val3, a*d*g == val4, b*e*h == val5, c*f*i == val6, a > 0, b > 0, c > 0, d > 0, e > 0, f > 0, g > 0, h > 0, i > 0, a < 10, b < 10, c < 10, d < 10, e < 10, f < 10, g < 10, h < 10, i < 10, a, b, c, d, e, f, g, h, i, Integers]


      mypuzzle2[80, 63, 72, 72, 48, 105]


      enter image description here



      How do I modify the code, so that it only returns with the answer with unique values of 1 to 9?



      Thanks.






      equation-solving







      share|improve this question













      I have a puzzle for example:




      Use 1 to 9, once only in the cells so that you obtain row and column products as shown:
      enter image description here




      mypuzzle2[val1_, val2_, val3_, val4_, val5_, val6_] := Solve[a*b*c == val1, d*e*f == val2, g*h*i == val3, a*d*g == val4, b*e*h == val5, c*f*i == val6, a > 0, b > 0, c > 0, d > 0, e > 0, f > 0, g > 0, h > 0, i > 0, a < 10, b < 10, c < 10, d < 10, e < 10, f < 10, g < 10, h < 10, i < 10, a, b, c, d, e, f, g, h, i, Integers]


      mypuzzle2[80, 63, 72, 72, 48, 105]


      enter image description here



      How do I modify the code, so that it only returns with the answer with unique values of 1 to 9?



      Thanks.






      equation-solving




      equation-solving






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 52 mins ago









      Chen Stats Yu

      2,4671333




      2,4671333




















          1 Answer
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          mypuzzle3[val1_, val2_, val3_, val4_, val5_, val6_] := 
           Select[Permutations[Range @ 9], With[p = Partition[#, 3], 
           And[Times @@@ p == val1, val2, val3, Times @@@ Transpose[p] == val4, val5, val6]] &]

          mypuzzle3[80, 63, 72, 72, 48, 105]



          2, 8, 5, 9, 1, 7, 4, 6, 3







          share|improve this answer






















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            1 Answer
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            active

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            active

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            up vote
            4
            down vote



            accepted










            mypuzzle3[val1_, val2_, val3_, val4_, val5_, val6_] := 
             Select[Permutations[Range @ 9], With[p = Partition[#, 3], 
             And[Times @@@ p == val1, val2, val3, Times @@@ Transpose[p] == val4, val5, val6]] &]

            mypuzzle3[80, 63, 72, 72, 48, 105]



            2, 8, 5, 9, 1, 7, 4, 6, 3







            share|improve this answer


























              up vote
              4
              down vote



              accepted










              mypuzzle3[val1_, val2_, val3_, val4_, val5_, val6_] := 
               Select[Permutations[Range @ 9], With[p = Partition[#, 3], 
               And[Times @@@ p == val1, val2, val3, Times @@@ Transpose[p] == val4, val5, val6]] &]

              mypuzzle3[80, 63, 72, 72, 48, 105]



              2, 8, 5, 9, 1, 7, 4, 6, 3







              share|improve this answer
























                up vote
                4
                down vote



                accepted







                up vote
                4
                down vote



                accepted






                mypuzzle3[val1_, val2_, val3_, val4_, val5_, val6_] := 
                 Select[Permutations[Range @ 9], With[p = Partition[#, 3], 
                 And[Times @@@ p == val1, val2, val3, Times @@@ Transpose[p] == val4, val5, val6]] &]

                mypuzzle3[80, 63, 72, 72, 48, 105]



                2, 8, 5, 9, 1, 7, 4, 6, 3







                share|improve this answer














                mypuzzle3[val1_, val2_, val3_, val4_, val5_, val6_] := 
                 Select[Permutations[Range @ 9], With[p = Partition[#, 3], 
                 And[Times @@@ p == val1, val2, val3, Times @@@ Transpose[p] == val4, val5, val6]] &]

                mypuzzle3[80, 63, 72, 72, 48, 105]



                2, 8, 5, 9, 1, 7, 4, 6, 3








                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 5 mins ago

























                answered 26 mins ago









                kglr

                160k8184384




                160k8184384



























                     

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