## 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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