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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