Using only 1s, make 29 with the minimum number of digits












1












$begingroup$


Operations permitted:




  • Standard operations: +, −, ×, ÷

  • Negation: −

  • Exponentiation of two numbers: x^y

  • Square root of a number: √

  • Factorial: !

  • Concatenation of the original digits: dd






mathematics calculation-puzzle formation-of-numbers







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$endgroup$

















    1












    $begingroup$


    Operations permitted:




    • Standard operations: +, −, ×, ÷

    • Negation: −

    • Exponentiation of two numbers: x^y

    • Square root of a number: √

    • Factorial: !

    • Concatenation of the original digits: dd






    mathematics calculation-puzzle formation-of-numbers







    share|improve this question







    New contributor




    Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$















      1












      1








      1





      $begingroup$


      Operations permitted:




      • Standard operations: +, −, ×, ÷

      • Negation: −

      • Exponentiation of two numbers: x^y

      • Square root of a number: √

      • Factorial: !

      • Concatenation of the original digits: dd






      mathematics calculation-puzzle formation-of-numbers







      share|improve this question







      New contributor




      Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      Operations permitted:




      • Standard operations: +, −, ×, ÷

      • Negation: −

      • Exponentiation of two numbers: x^y

      • Square root of a number: √

      • Factorial: !

      • Concatenation of the original digits: dd






      mathematics calculation-puzzle formation-of-numbers




      mathematics calculation-puzzle formation-of-numbers






      share|improve this question







      New contributor




      Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question







      New contributor




      Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question






      New contributor




      Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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      asked 54 mins ago









      Allan CaoAllan Cao

      1063




      1063




      New contributor




      Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Allan Cao is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






















          2 Answers
          2






          active

          oldest

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          4












          $begingroup$

          Here's a 7 digits solution:




          7 digits: (11-1)x(1+1+1)-1







          share|improve this answer









          $endgroup$













          • $begingroup$
            That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
            $endgroup$
            – Allan Cao
            21 mins ago










          • $begingroup$
            Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
            $endgroup$
            – Dr Xorile
            18 mins ago










          • $begingroup$
            The paper uses different rules.
            $endgroup$
            – Allan Cao
            8 mins ago



















          2












          $begingroup$

          Lowest I managed so far is 9 digits:




          (1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1



          11*(1 + 1 + 1) - (1 + 1 + 1 + 1)




          Some other ways I came up with:




          (1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)



          (1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)



          (1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)



          11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)







          share|improve this answer











          $endgroup$













            Your Answer





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            2 Answers
            2






            active

            oldest

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            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            4












            $begingroup$

            Here's a 7 digits solution:




            7 digits: (11-1)x(1+1+1)-1







            share|improve this answer









            $endgroup$













            • $begingroup$
              That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
              $endgroup$
              – Allan Cao
              21 mins ago










            • $begingroup$
              Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
              $endgroup$
              – Dr Xorile
              18 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              8 mins ago
















            4












            $begingroup$

            Here's a 7 digits solution:




            7 digits: (11-1)x(1+1+1)-1







            share|improve this answer









            $endgroup$













            • $begingroup$
              That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
              $endgroup$
              – Allan Cao
              21 mins ago










            • $begingroup$
              Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
              $endgroup$
              – Dr Xorile
              18 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              8 mins ago














            4












            4








            4





            $begingroup$

            Here's a 7 digits solution:




            7 digits: (11-1)x(1+1+1)-1







            share|improve this answer









            $endgroup$



            Here's a 7 digits solution:




            7 digits: (11-1)x(1+1+1)-1








            share|improve this answer












            share|improve this answer



            share|improve this answer










            answered 31 mins ago









            Dr XorileDr Xorile

            12.9k22569




            12.9k22569












            • $begingroup$
              That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
              $endgroup$
              – Allan Cao
              21 mins ago










            • $begingroup$
              Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
              $endgroup$
              – Dr Xorile
              18 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              8 mins ago


















            • $begingroup$
              That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
              $endgroup$
              – Allan Cao
              21 mins ago










            • $begingroup$
              Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
              $endgroup$
              – Dr Xorile
              18 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              8 mins ago
















            $begingroup$
            That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
            $endgroup$
            – Allan Cao
            21 mins ago




            $begingroup$
            That is the minimum I achieved by referencing the Single Digit Representations of Natural Numbers paper. Hopefully 6 is possible.
            $endgroup$
            – Allan Cao
            21 mins ago












            $begingroup$
            Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
            $endgroup$
            – Dr Xorile
            18 mins ago




            $begingroup$
            Do you mean that allowing concatenations should reduce it from 7 to 6? Or are the constraints the same in the paper you cite as in the question above?
            $endgroup$
            – Dr Xorile
            18 mins ago












            $begingroup$
            The paper uses different rules.
            $endgroup$
            – Allan Cao
            8 mins ago




            $begingroup$
            The paper uses different rules.
            $endgroup$
            – Allan Cao
            8 mins ago











            2












            $begingroup$

            Lowest I managed so far is 9 digits:




            (1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1



            11*(1 + 1 + 1) - (1 + 1 + 1 + 1)




            Some other ways I came up with:




            (1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)



            (1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)



            (1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)



            11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)







            share|improve this answer











            $endgroup$


















              2












              $begingroup$

              Lowest I managed so far is 9 digits:




              (1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1



              11*(1 + 1 + 1) - (1 + 1 + 1 + 1)




              Some other ways I came up with:




              (1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)



              (1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)



              (1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)



              11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)







              share|improve this answer











              $endgroup$
















                2












                2








                2





                $begingroup$

                Lowest I managed so far is 9 digits:




                (1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1



                11*(1 + 1 + 1) - (1 + 1 + 1 + 1)




                Some other ways I came up with:




                (1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)



                (1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)



                (1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)



                11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)







                share|improve this answer











                $endgroup$



                Lowest I managed so far is 9 digits:




                (1 + 1 + 1 + 1)! + 1 + 1 + 1 + 1 + 1



                11*(1 + 1 + 1) - (1 + 1 + 1 + 1)




                Some other ways I came up with:




                (1 + 1)^(1 + 1 + 1 + 1 + 1) - 1 - 1 - 1 (10 digits)



                (1 + 1 + 1 + 1 + 1)!/(1 + 1 + 1 + 1) - 1 (10 digits)



                (1 + 1 + 1 + 1 + 1)^(1 + 1) + 1 + 1 + 1 + 1 (11 digits)



                11*(1 + 1) + 1 + 1 + 1 + 1 + 1 + 1 + 1 (11 digits)








                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 33 mins ago

























                answered 41 mins ago









                simonzacksimonzack

                267110




                267110






















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