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










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












    $begingroup$


    Operations permitted:




    • Standard operations: +, −, ×, ÷

    • Negation: −

    • Exponentiation of two numbers: x^y

    • Square root of a number: √

    • Factorial: !

    • Concatenation of the original digits: dd










    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










      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






      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.
      Check out our Code of Conduct.









      asked 1 hour 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

          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
            43 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
            40 mins ago










          • $begingroup$
            The paper uses different rules.
            $endgroup$
            – Allan Cao
            30 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





            StackExchange.ifUsing("editor", function () {
            return StackExchange.using("mathjaxEditing", function () {
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            });
            });
            }, "mathjax-editing");

            StackExchange.ready(function() {
            var channelOptions = {
            tags: "".split(" "),
            id: "559"
            };
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function() {
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled) {
            StackExchange.using("snippets", function() {
            createEditor();
            });
            }
            else {
            createEditor();
            }
            });

            function createEditor() {
            StackExchange.prepareEditor({
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader: {
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            },
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            });


            }
            });






            Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.










            draft saved

            draft discarded


















            StackExchange.ready(
            function () {
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f80050%2fusing-only-1s-make-29-with-the-minimum-number-of-digits%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            2 Answers
            2






            active

            oldest

            votes








            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
              43 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
              40 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              30 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
              43 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
              40 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              30 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 53 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
              43 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
              40 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              30 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
              43 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
              40 mins ago










            • $begingroup$
              The paper uses different rules.
              $endgroup$
              – Allan Cao
              30 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
            43 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
            43 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
            40 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
            40 mins ago












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




            $begingroup$
            The paper uses different rules.
            $endgroup$
            – Allan Cao
            30 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 55 mins ago

























                answered 1 hour ago









                simonzacksimonzack

                267110




                267110






















                    Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.










                    draft saved

                    draft discarded


















                    Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.













                    Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.












                    Allan Cao is a new contributor. Be nice, and check out our Code of Conduct.
















                    Thanks for contributing an answer to Puzzling Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid



                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.


                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function () {
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fpuzzling.stackexchange.com%2fquestions%2f80050%2fusing-only-1s-make-29-with-the-minimum-number-of-digits%23new-answer', 'question_page');
                    }
                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    Popular posts from this blog

                    Liste der Baudenkmale in Friedland (Mecklenburg)

                    Single-Malt-Whisky

                    Czorneboh