Lonesome-Eight Challenge

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from page 55 of Martin Garner's My Best Mathematical and Logic Puzzles.

" 27. In long division, when two digits are brought down instead of one, there must
be a zero in the quotient. This occurs twice, so we know at once that the quotient
is x080x. When the divisor is multiplied by the quotient's last digit, the product is a
four-digit number. The quotient's last digit must therefore be 9, because eight times
the divisor is a three-digit number.
The divisor must be less than 125 because eight times 125 is 1,000, a four-digit
number. We now can deduce that the quotient's first digit must be more than 7, for
seven times a divisor less than 125 would give a prod uct that would leave more
than two digits after it was subtracted from the first four digits in the dividend. This
first digit cannot be 9 (which gives a four-digit number when the divisor is multiplied
by it), so it must be 8, making the full quotient 80809.
The divisor must be more than 123 because 80809 times 123 is a seven-digit number
and our dividend has eight digits. The only number between 123 and 125 is 124."

BEST!
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