From 2019 to digits












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Is it possible to obtain the digits from 0 to 9 starting from 2019 and using its digits in the same order, together with the usual operations +, *, -, /, concatenation of digits, and the less usual operators ^, !, sqrt(), int()? For example, 1 = 20-19. Unary minus is allowed too.



I manage to use only basic operations and elevation to a power for all digits except 4 and 5, but maybe somebody will do better!






arithmetic







share|improve this question









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    1












    $begingroup$


    Is it possible to obtain the digits from 0 to 9 starting from 2019 and using its digits in the same order, together with the usual operations +, *, -, /, concatenation of digits, and the less usual operators ^, !, sqrt(), int()? For example, 1 = 20-19. Unary minus is allowed too.



    I manage to use only basic operations and elevation to a power for all digits except 4 and 5, but maybe somebody will do better!






    arithmetic







    share|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      Is it possible to obtain the digits from 0 to 9 starting from 2019 and using its digits in the same order, together with the usual operations +, *, -, /, concatenation of digits, and the less usual operators ^, !, sqrt(), int()? For example, 1 = 20-19. Unary minus is allowed too.



      I manage to use only basic operations and elevation to a power for all digits except 4 and 5, but maybe somebody will do better!






      arithmetic







      share|improve this question









      $endgroup$




      Is it possible to obtain the digits from 0 to 9 starting from 2019 and using its digits in the same order, together with the usual operations +, *, -, /, concatenation of digits, and the less usual operators ^, !, sqrt(), int()? For example, 1 = 20-19. Unary minus is allowed too.



      I manage to use only basic operations and elevation to a power for all digits except 4 and 5, but maybe somebody will do better!






      arithmetic




      arithmetic






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked Dec 23 '18 at 20:45









      maumau

      1,0041233




      1,0041233






















          1 Answer
          1






          active

          oldest

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          5












          $begingroup$


          $0 = 2 cdot 0 cdot 1 cdot 9$

          $1 = 20 - 19$

          $2 = 2^0 + 1^9$

          $3 = 2+0+1^9$

          $4 = lfloor sqrt{20} rfloor + lfloor 1/9 rfloor$

          $5 = 2 + 0 cdot 1 + sqrt{9}$

          $6 = -(2+0+1) + 9$

          $7 = -(2+0 cdot 1) + 9$

          $8 = -(2 cdot 0 + 1) + 9$

          $9 = -(2 cdot 0 cdot 1) + 9$







          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            @deepthought Fixed.
            $endgroup$
            – Display name
            Dec 23 '18 at 21:29






          • 3




            $begingroup$
            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            $endgroup$
            – mau
            Dec 23 '18 at 21:48






          • 1




            $begingroup$
            A few more for 4 and 5: $lfloorsqrt{sqrt{20times19}}rfloor=4$, $lceilsqrt{sqrt{20times19}}rceil=5$ , $lceilsqrt{2+0+1+9}rceil=4$ , $lfloorsqrt{2+0+19}rfloor=4$ , $lceilsqrt{2+0+19}rceil=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:02








          • 1




            $begingroup$
            and $lfloorsqrt{201}rfloor-9=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:05






          • 1




            $begingroup$
            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            $endgroup$
            – Display name
            Dec 23 '18 at 22:55













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          1 Answer
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          active

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          5












          $begingroup$


          $0 = 2 cdot 0 cdot 1 cdot 9$

          $1 = 20 - 19$

          $2 = 2^0 + 1^9$

          $3 = 2+0+1^9$

          $4 = lfloor sqrt{20} rfloor + lfloor 1/9 rfloor$

          $5 = 2 + 0 cdot 1 + sqrt{9}$

          $6 = -(2+0+1) + 9$

          $7 = -(2+0 cdot 1) + 9$

          $8 = -(2 cdot 0 + 1) + 9$

          $9 = -(2 cdot 0 cdot 1) + 9$







          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            @deepthought Fixed.
            $endgroup$
            – Display name
            Dec 23 '18 at 21:29






          • 3




            $begingroup$
            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            $endgroup$
            – mau
            Dec 23 '18 at 21:48






          • 1




            $begingroup$
            A few more for 4 and 5: $lfloorsqrt{sqrt{20times19}}rfloor=4$, $lceilsqrt{sqrt{20times19}}rceil=5$ , $lceilsqrt{2+0+1+9}rceil=4$ , $lfloorsqrt{2+0+19}rfloor=4$ , $lceilsqrt{2+0+19}rceil=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:02








          • 1




            $begingroup$
            and $lfloorsqrt{201}rfloor-9=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:05






          • 1




            $begingroup$
            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            $endgroup$
            – Display name
            Dec 23 '18 at 22:55


















          5












          $begingroup$


          $0 = 2 cdot 0 cdot 1 cdot 9$

          $1 = 20 - 19$

          $2 = 2^0 + 1^9$

          $3 = 2+0+1^9$

          $4 = lfloor sqrt{20} rfloor + lfloor 1/9 rfloor$

          $5 = 2 + 0 cdot 1 + sqrt{9}$

          $6 = -(2+0+1) + 9$

          $7 = -(2+0 cdot 1) + 9$

          $8 = -(2 cdot 0 + 1) + 9$

          $9 = -(2 cdot 0 cdot 1) + 9$







          share|improve this answer











          $endgroup$









          • 1




            $begingroup$
            @deepthought Fixed.
            $endgroup$
            – Display name
            Dec 23 '18 at 21:29






          • 3




            $begingroup$
            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            $endgroup$
            – mau
            Dec 23 '18 at 21:48






          • 1




            $begingroup$
            A few more for 4 and 5: $lfloorsqrt{sqrt{20times19}}rfloor=4$, $lceilsqrt{sqrt{20times19}}rceil=5$ , $lceilsqrt{2+0+1+9}rceil=4$ , $lfloorsqrt{2+0+19}rfloor=4$ , $lceilsqrt{2+0+19}rceil=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:02








          • 1




            $begingroup$
            and $lfloorsqrt{201}rfloor-9=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:05






          • 1




            $begingroup$
            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            $endgroup$
            – Display name
            Dec 23 '18 at 22:55
















          5












          5








          5





          $begingroup$


          $0 = 2 cdot 0 cdot 1 cdot 9$

          $1 = 20 - 19$

          $2 = 2^0 + 1^9$

          $3 = 2+0+1^9$

          $4 = lfloor sqrt{20} rfloor + lfloor 1/9 rfloor$

          $5 = 2 + 0 cdot 1 + sqrt{9}$

          $6 = -(2+0+1) + 9$

          $7 = -(2+0 cdot 1) + 9$

          $8 = -(2 cdot 0 + 1) + 9$

          $9 = -(2 cdot 0 cdot 1) + 9$







          share|improve this answer











          $endgroup$




          $0 = 2 cdot 0 cdot 1 cdot 9$

          $1 = 20 - 19$

          $2 = 2^0 + 1^9$

          $3 = 2+0+1^9$

          $4 = lfloor sqrt{20} rfloor + lfloor 1/9 rfloor$

          $5 = 2 + 0 cdot 1 + sqrt{9}$

          $6 = -(2+0+1) + 9$

          $7 = -(2+0 cdot 1) + 9$

          $8 = -(2 cdot 0 + 1) + 9$

          $9 = -(2 cdot 0 cdot 1) + 9$








          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited Dec 24 '18 at 5:20









          S. M.

          953419




          953419










          answered Dec 23 '18 at 21:13









          Display nameDisplay name

          1,000217




          1,000217








          • 1




            $begingroup$
            @deepthought Fixed.
            $endgroup$
            – Display name
            Dec 23 '18 at 21:29






          • 3




            $begingroup$
            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            $endgroup$
            – mau
            Dec 23 '18 at 21:48






          • 1




            $begingroup$
            A few more for 4 and 5: $lfloorsqrt{sqrt{20times19}}rfloor=4$, $lceilsqrt{sqrt{20times19}}rceil=5$ , $lceilsqrt{2+0+1+9}rceil=4$ , $lfloorsqrt{2+0+19}rfloor=4$ , $lceilsqrt{2+0+19}rceil=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:02








          • 1




            $begingroup$
            and $lfloorsqrt{201}rfloor-9=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:05






          • 1




            $begingroup$
            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            $endgroup$
            – Display name
            Dec 23 '18 at 22:55
















          • 1




            $begingroup$
            @deepthought Fixed.
            $endgroup$
            – Display name
            Dec 23 '18 at 21:29






          • 3




            $begingroup$
            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            $endgroup$
            – mau
            Dec 23 '18 at 21:48






          • 1




            $begingroup$
            A few more for 4 and 5: $lfloorsqrt{sqrt{20times19}}rfloor=4$, $lceilsqrt{sqrt{20times19}}rceil=5$ , $lceilsqrt{2+0+1+9}rceil=4$ , $lfloorsqrt{2+0+19}rfloor=4$ , $lceilsqrt{2+0+19}rceil=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:02








          • 1




            $begingroup$
            and $lfloorsqrt{201}rfloor-9=5$
            $endgroup$
            – JonMark Perry
            Dec 23 '18 at 22:05






          • 1




            $begingroup$
            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            $endgroup$
            – Display name
            Dec 23 '18 at 22:55










          1




          1




          $begingroup$
          @deepthought Fixed.
          $endgroup$
          – Display name
          Dec 23 '18 at 21:29




          $begingroup$
          @deepthought Fixed.
          $endgroup$
          – Display name
          Dec 23 '18 at 21:29




          3




          3




          $begingroup$
          Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
          $endgroup$
          – mau
          Dec 23 '18 at 21:48




          $begingroup$
          Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
          $endgroup$
          – mau
          Dec 23 '18 at 21:48




          1




          1




          $begingroup$
          A few more for 4 and 5: $lfloorsqrt{sqrt{20times19}}rfloor=4$, $lceilsqrt{sqrt{20times19}}rceil=5$ , $lceilsqrt{2+0+1+9}rceil=4$ , $lfloorsqrt{2+0+19}rfloor=4$ , $lceilsqrt{2+0+19}rceil=5$
          $endgroup$
          – JonMark Perry
          Dec 23 '18 at 22:02






          $begingroup$
          A few more for 4 and 5: $lfloorsqrt{sqrt{20times19}}rfloor=4$, $lceilsqrt{sqrt{20times19}}rceil=5$ , $lceilsqrt{2+0+1+9}rceil=4$ , $lfloorsqrt{2+0+19}rfloor=4$ , $lceilsqrt{2+0+19}rceil=5$
          $endgroup$
          – JonMark Perry
          Dec 23 '18 at 22:02






          1




          1




          $begingroup$
          and $lfloorsqrt{201}rfloor-9=5$
          $endgroup$
          – JonMark Perry
          Dec 23 '18 at 22:05




          $begingroup$
          and $lfloorsqrt{201}rfloor-9=5$
          $endgroup$
          – JonMark Perry
          Dec 23 '18 at 22:05




          1




          1




          $begingroup$
          Fun fact: $-lfloor -x rfloor = lceil x rceil.$
          $endgroup$
          – Display name
          Dec 23 '18 at 22:55






          $begingroup$
          Fun fact: $-lfloor -x rfloor = lceil x rceil.$
          $endgroup$
          – Display name
          Dec 23 '18 at 22:55




















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