From 2019 to digits












1














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







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    1














    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

























      1












      1








      1







      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













      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 6 hours ago









      mau

      9941233




      9941233






















          1 Answer
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          4














          $0 = 2 cdot 0 cdot 1 cdot 9$



          $1 = 20 - 19$



          $2 = 2^0 + 1^9$



          $3 = 2+0+1^9$



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



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



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



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



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



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





          share























          • Ok for the first three, but I think you're not supposed to rearrange the digits
            – deep thought
            5 hours ago






          • 1




            @deepthought Fixed.
            – Display name
            5 hours ago






          • 1




            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            – mau
            5 hours ago






          • 1




            and $lfloorsqrt{201}rfloor-9=5$
            – JonMark Perry
            5 hours ago






          • 1




            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            – Display name
            4 hours ago













          Your Answer





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          4














          $0 = 2 cdot 0 cdot 1 cdot 9$



          $1 = 20 - 19$



          $2 = 2^0 + 1^9$



          $3 = 2+0+1^9$



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



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



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



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



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



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





          share























          • Ok for the first three, but I think you're not supposed to rearrange the digits
            – deep thought
            5 hours ago






          • 1




            @deepthought Fixed.
            – Display name
            5 hours ago






          • 1




            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            – mau
            5 hours ago






          • 1




            and $lfloorsqrt{201}rfloor-9=5$
            – JonMark Perry
            5 hours ago






          • 1




            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            – Display name
            4 hours ago


















          4














          $0 = 2 cdot 0 cdot 1 cdot 9$



          $1 = 20 - 19$



          $2 = 2^0 + 1^9$



          $3 = 2+0+1^9$



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



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



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



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



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



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





          share























          • Ok for the first three, but I think you're not supposed to rearrange the digits
            – deep thought
            5 hours ago






          • 1




            @deepthought Fixed.
            – Display name
            5 hours ago






          • 1




            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            – mau
            5 hours ago






          • 1




            and $lfloorsqrt{201}rfloor-9=5$
            – JonMark Perry
            5 hours ago






          • 1




            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            – Display name
            4 hours ago
















          4












          4








          4






          $0 = 2 cdot 0 cdot 1 cdot 9$



          $1 = 20 - 19$



          $2 = 2^0 + 1^9$



          $3 = 2+0+1^9$



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



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



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



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



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



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





          share














          $0 = 2 cdot 0 cdot 1 cdot 9$



          $1 = 20 - 19$



          $2 = 2^0 + 1^9$



          $3 = 2+0+1^9$



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



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



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



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



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



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






          share













          share


          share








          edited 5 hours ago

























          answered 5 hours ago









          Display name

          714216




          714216












          • Ok for the first three, but I think you're not supposed to rearrange the digits
            – deep thought
            5 hours ago






          • 1




            @deepthought Fixed.
            – Display name
            5 hours ago






          • 1




            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            – mau
            5 hours ago






          • 1




            and $lfloorsqrt{201}rfloor-9=5$
            – JonMark Perry
            5 hours ago






          • 1




            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            – Display name
            4 hours ago




















          • Ok for the first three, but I think you're not supposed to rearrange the digits
            – deep thought
            5 hours ago






          • 1




            @deepthought Fixed.
            – Display name
            5 hours ago






          • 1




            Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
            – mau
            5 hours ago






          • 1




            and $lfloorsqrt{201}rfloor-9=5$
            – JonMark Perry
            5 hours ago






          • 1




            Fun fact: $-lfloor -x rfloor = lceil x rceil.$
            – Display name
            4 hours ago


















          Ok for the first three, but I think you're not supposed to rearrange the digits
          – deep thought
          5 hours ago




          Ok for the first three, but I think you're not supposed to rearrange the digits
          – deep thought
          5 hours ago




          1




          1




          @deepthought Fixed.
          – Display name
          5 hours ago




          @deepthought Fixed.
          – Display name
          5 hours ago




          1




          1




          Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
          – mau
          5 hours ago




          Nice! 4 may also be $2cdot 0 + 1 + sqrt 9$
          – mau
          5 hours ago




          1




          1




          and $lfloorsqrt{201}rfloor-9=5$
          – JonMark Perry
          5 hours ago




          and $lfloorsqrt{201}rfloor-9=5$
          – JonMark Perry
          5 hours ago




          1




          1




          Fun fact: $-lfloor -x rfloor = lceil x rceil.$
          – Display name
          4 hours ago






          Fun fact: $-lfloor -x rfloor = lceil x rceil.$
          – Display name
          4 hours ago




















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