Solve this long division problem, where each of the x's represent a decimal digit from 0 to 9, whether same or different. None of the numbers may contain any leading zero.

              x x x x x
        -------------------
x x |  x x x x 0 0 0
           x x
        -------------------
           x x x
              x x
        --------------------
                 x 0
                 x x
        --------------------
                 x x 0
                 x x x
        ---------------------
                       x 0
                       x 0
       ----------------------

Note: Try to derive a non computer program assisted method, although computer program/spreadsheet solutions are welcome.

DEFDBL A-Z
FOR dnd = 1000000 TO 9999000 STEP 1000
 FOR dvr = 10 TO 99
   IF dnd MOD dvr = 0 THEN
 
    q = (dnd \ 10000) \ dvr
    r = (dnd \ 10000) MOD dvr
    IF q >= 1 AND q <= 9 AND q * dvr >= 10 AND q * dvr <= 99 AND r >= 10 AND r <= 99 THEN
      d = r * 10 + (dnd \ 1000) MOD 10
      q = d \ dvr: r = d MOD dvr
      s = q * dvr
      IF s >= 10 AND s <= 99 THEN
        diff = d - s
        IF diff >= 1 AND diff <= 9 THEN
         d = 10 * diff
         q = d \ dvr: r = d MOD dvr
         s = q * dvr
         IF s >= 10 AND s <= 99 THEN
           diff = d - s
           IF diff >= 10 AND diff <= 99 THEN
            d = 10 * diff
            q = d \ dvr: r = d MOD dvr
            s = q * dvr
            IF s >= 100 AND s <= 999 THEN
              diff = d - s
              IF diff >= 1 AND diff <= 9 THEN
                d = 10 * diff
                q = d \ dvr: r = d MOD dvr
                s = q * dvr
                IF r = 0 THEN
                   PRINT dvr, dnd
                END IF
              END IF
            END IF
           END IF
         END IF
        END IF
      END IF
    END IF

   END IF
 NEXT
NEXT
PRINT ct

finds

16 divided into 1062000

which comes out as

       66375
16 | 1062000
      96
      102
       96
        60
        48
        120
        112
         80
         80

Posted by Charlie on 2009-01-12 17:25:26