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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