For what x can we solve $1,2,3,x=5$












5












$begingroup$


This is a variation on the formation of numbers theme.




Given $1, 2, 3, x$ in order, and the operations plus, minus, times, divide, and brackets, what single digits can x NOT be?




i.e. find a solution for $x$ from $0$ to $9$, or prove there is no solution.



For example if $x=4$ we have:




$ (1+2)times3-4=5$







mathematics formation-of-numbers







share|improve this question









$endgroup$

















    5












    $begingroup$


    This is a variation on the formation of numbers theme.




    Given $1, 2, 3, x$ in order, and the operations plus, minus, times, divide, and brackets, what single digits can x NOT be?




    i.e. find a solution for $x$ from $0$ to $9$, or prove there is no solution.



    For example if $x=4$ we have:




    $ (1+2)times3-4=5$







    mathematics formation-of-numbers







    share|improve this question









    $endgroup$















      5












      5








      5


      1



      $begingroup$


      This is a variation on the formation of numbers theme.




      Given $1, 2, 3, x$ in order, and the operations plus, minus, times, divide, and brackets, what single digits can x NOT be?




      i.e. find a solution for $x$ from $0$ to $9$, or prove there is no solution.



      For example if $x=4$ we have:




      $ (1+2)times3-4=5$







      mathematics formation-of-numbers







      share|improve this question









      $endgroup$




      This is a variation on the formation of numbers theme.




      Given $1, 2, 3, x$ in order, and the operations plus, minus, times, divide, and brackets, what single digits can x NOT be?




      i.e. find a solution for $x$ from $0$ to $9$, or prove there is no solution.



      For example if $x=4$ we have:




      $ (1+2)times3-4=5$







      mathematics formation-of-numbers




      mathematics formation-of-numbers






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 23 hours ago









      JonMark PerryJonMark Perry

      20k64096




      20k64096






















          1 Answer
          1






          active

          oldest

          votes


















          10












          $begingroup$

          It is possible for x = {0-9}.




          $X=0: ;;1 times 2 + 3 + 0 = 5$
          $X=1: ;;1 times 2 times3 - 1 = 5$
          $X=2: ;;1 + 2 times 3 - 2 = 5$
          $X=3: ;;1 - 2 + 3 + 3 = 5$
          $X=4: ;;(1 + 2) times 3 - 4 = 5$
          $X=5: ;;(1 + 2) / 3 times 5 = 5$
          $X=6: ;;1 + 2 / 3 times 6 = 5$
          $X=7: ;;1 / 2 times (3 + 7) = 5$
          $X=8: ;;(1 - 2) times 3 + 8 = 5$
          $X=9: ;;1 - 2 - 3 + 9 = 5$







          share|improve this answer











          $endgroup$













          • $begingroup$
            they have to be in order
            $endgroup$
            – JonMark Perry
            22 hours ago










          • $begingroup$
            and done! Here you go!
            $endgroup$
            – Arch2K
            22 hours ago






          • 1




            $begingroup$
            I don't think negation is allowed. A subtraction (minus) operation requires two operands.
            $endgroup$
            – Amorydai
            22 hours ago










          • $begingroup$
            Not sure if it was required, but answer has since been fixed to remove negation.
            $endgroup$
            – Arch2K
            22 hours ago










          • $begingroup$
            You don't need the brackets in lines X=1 and X=2.
            $endgroup$
            – Arnaud Mortier
            17 hours ago













          Your Answer





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          1 Answer
          1






          active

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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          10












          $begingroup$

          It is possible for x = {0-9}.




          $X=0: ;;1 times 2 + 3 + 0 = 5$
          $X=1: ;;1 times 2 times3 - 1 = 5$
          $X=2: ;;1 + 2 times 3 - 2 = 5$
          $X=3: ;;1 - 2 + 3 + 3 = 5$
          $X=4: ;;(1 + 2) times 3 - 4 = 5$
          $X=5: ;;(1 + 2) / 3 times 5 = 5$
          $X=6: ;;1 + 2 / 3 times 6 = 5$
          $X=7: ;;1 / 2 times (3 + 7) = 5$
          $X=8: ;;(1 - 2) times 3 + 8 = 5$
          $X=9: ;;1 - 2 - 3 + 9 = 5$







          share|improve this answer











          $endgroup$













          • $begingroup$
            they have to be in order
            $endgroup$
            – JonMark Perry
            22 hours ago










          • $begingroup$
            and done! Here you go!
            $endgroup$
            – Arch2K
            22 hours ago






          • 1




            $begingroup$
            I don't think negation is allowed. A subtraction (minus) operation requires two operands.
            $endgroup$
            – Amorydai
            22 hours ago










          • $begingroup$
            Not sure if it was required, but answer has since been fixed to remove negation.
            $endgroup$
            – Arch2K
            22 hours ago










          • $begingroup$
            You don't need the brackets in lines X=1 and X=2.
            $endgroup$
            – Arnaud Mortier
            17 hours ago


















          10












          $begingroup$

          It is possible for x = {0-9}.




          $X=0: ;;1 times 2 + 3 + 0 = 5$
          $X=1: ;;1 times 2 times3 - 1 = 5$
          $X=2: ;;1 + 2 times 3 - 2 = 5$
          $X=3: ;;1 - 2 + 3 + 3 = 5$
          $X=4: ;;(1 + 2) times 3 - 4 = 5$
          $X=5: ;;(1 + 2) / 3 times 5 = 5$
          $X=6: ;;1 + 2 / 3 times 6 = 5$
          $X=7: ;;1 / 2 times (3 + 7) = 5$
          $X=8: ;;(1 - 2) times 3 + 8 = 5$
          $X=9: ;;1 - 2 - 3 + 9 = 5$







          share|improve this answer











          $endgroup$













          • $begingroup$
            they have to be in order
            $endgroup$
            – JonMark Perry
            22 hours ago










          • $begingroup$
            and done! Here you go!
            $endgroup$
            – Arch2K
            22 hours ago






          • 1




            $begingroup$
            I don't think negation is allowed. A subtraction (minus) operation requires two operands.
            $endgroup$
            – Amorydai
            22 hours ago










          • $begingroup$
            Not sure if it was required, but answer has since been fixed to remove negation.
            $endgroup$
            – Arch2K
            22 hours ago










          • $begingroup$
            You don't need the brackets in lines X=1 and X=2.
            $endgroup$
            – Arnaud Mortier
            17 hours ago
















          10












          10








          10





          $begingroup$

          It is possible for x = {0-9}.




          $X=0: ;;1 times 2 + 3 + 0 = 5$
          $X=1: ;;1 times 2 times3 - 1 = 5$
          $X=2: ;;1 + 2 times 3 - 2 = 5$
          $X=3: ;;1 - 2 + 3 + 3 = 5$
          $X=4: ;;(1 + 2) times 3 - 4 = 5$
          $X=5: ;;(1 + 2) / 3 times 5 = 5$
          $X=6: ;;1 + 2 / 3 times 6 = 5$
          $X=7: ;;1 / 2 times (3 + 7) = 5$
          $X=8: ;;(1 - 2) times 3 + 8 = 5$
          $X=9: ;;1 - 2 - 3 + 9 = 5$







          share|improve this answer











          $endgroup$



          It is possible for x = {0-9}.




          $X=0: ;;1 times 2 + 3 + 0 = 5$
          $X=1: ;;1 times 2 times3 - 1 = 5$
          $X=2: ;;1 + 2 times 3 - 2 = 5$
          $X=3: ;;1 - 2 + 3 + 3 = 5$
          $X=4: ;;(1 + 2) times 3 - 4 = 5$
          $X=5: ;;(1 + 2) / 3 times 5 = 5$
          $X=6: ;;1 + 2 / 3 times 6 = 5$
          $X=7: ;;1 / 2 times (3 + 7) = 5$
          $X=8: ;;(1 - 2) times 3 + 8 = 5$
          $X=9: ;;1 - 2 - 3 + 9 = 5$








          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 14 hours ago

























          answered 22 hours ago









          Arch2KArch2K

          76412




          76412












          • $begingroup$
            they have to be in order
            $endgroup$
            – JonMark Perry
            22 hours ago










          • $begingroup$
            and done! Here you go!
            $endgroup$
            – Arch2K
            22 hours ago






          • 1




            $begingroup$
            I don't think negation is allowed. A subtraction (minus) operation requires two operands.
            $endgroup$
            – Amorydai
            22 hours ago










          • $begingroup$
            Not sure if it was required, but answer has since been fixed to remove negation.
            $endgroup$
            – Arch2K
            22 hours ago










          • $begingroup$
            You don't need the brackets in lines X=1 and X=2.
            $endgroup$
            – Arnaud Mortier
            17 hours ago




















          • $begingroup$
            they have to be in order
            $endgroup$
            – JonMark Perry
            22 hours ago










          • $begingroup$
            and done! Here you go!
            $endgroup$
            – Arch2K
            22 hours ago






          • 1




            $begingroup$
            I don't think negation is allowed. A subtraction (minus) operation requires two operands.
            $endgroup$
            – Amorydai
            22 hours ago










          • $begingroup$
            Not sure if it was required, but answer has since been fixed to remove negation.
            $endgroup$
            – Arch2K
            22 hours ago










          • $begingroup$
            You don't need the brackets in lines X=1 and X=2.
            $endgroup$
            – Arnaud Mortier
            17 hours ago


















          $begingroup$
          they have to be in order
          $endgroup$
          – JonMark Perry
          22 hours ago




          $begingroup$
          they have to be in order
          $endgroup$
          – JonMark Perry
          22 hours ago












          $begingroup$
          and done! Here you go!
          $endgroup$
          – Arch2K
          22 hours ago




          $begingroup$
          and done! Here you go!
          $endgroup$
          – Arch2K
          22 hours ago




          1




          1




          $begingroup$
          I don't think negation is allowed. A subtraction (minus) operation requires two operands.
          $endgroup$
          – Amorydai
          22 hours ago




          $begingroup$
          I don't think negation is allowed. A subtraction (minus) operation requires two operands.
          $endgroup$
          – Amorydai
          22 hours ago












          $begingroup$
          Not sure if it was required, but answer has since been fixed to remove negation.
          $endgroup$
          – Arch2K
          22 hours ago




          $begingroup$
          Not sure if it was required, but answer has since been fixed to remove negation.
          $endgroup$
          – Arch2K
          22 hours ago












          $begingroup$
          You don't need the brackets in lines X=1 and X=2.
          $endgroup$
          – Arnaud Mortier
          17 hours ago






          $begingroup$
          You don't need the brackets in lines X=1 and X=2.
          $endgroup$
          – Arnaud Mortier
          17 hours ago




















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