Solution to: Long Division

We will indicate the numbers in the long division in the manner shown below:

. . . / . . . . . . . . \ . . 8 . .             A /  B      \ C
          . . .                                      D
        -------                                     ---
            . . . .                                    E
              . . .                                    F
            -------                                   ---
                . . . .                                  G
                . . . .                                  H
                -------                                 ---
                      0                                  0

For E and G two digits have been brought down, therefore both the second and the fourth digits of C are 0.

Because F consists of three digits and equals the outcome of 8 times A, A must be smaller than 1000/8=125. Number H consists of four digits and is the product of number A and the last digit of C. Therefore, H is at least 1000, and because A is smaller than 125, the last digit of C must be 9. Moreover, A must be at least 1000/9, so be larger than 111.

Because the number D is subtracted from a number of four digits and the outcome consists of two digits, the first digit of D must be 9. This is possible only if the first digit of C is 8.

Now we know that the number C equals 80809 and number B is at least 10000000. From this, it follows that A is at least 124. Because we also know that A lies between 111 and 125, A equals 124.

The complete long division can now be filled in:

1 2 4 / 1 0 0 2 0 3 1 6 \ 8 0 8 0 9
          9 9 2
        -------
            1 0 0 3
              9 9 2
            -------
                1 1 1 6
                1 1 1 6
                -------
                      0

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