Complete the division

Question

Every dot represents a number . Now find all the numbers. I found this question in the social networks and it is really interesting problem. Also it has only one answer. I tried many ways to solve it but didn't get any result at all .

Answer 1

You can see on the left that only three multiples of the divisor $d$ have been subtracted off the dividend $a$ in the long division. In two cases, that was a three-digit number being subtracted from a four-digit number, and in the last case it was a four-digit number being subtracted to complete the division.

From the one digit supplied ($8$) in the quotient $q$, we know that $8d<1000$ so for the four digit case $9d\ge 1000$. Since we started with a three-digit subtraction from a four-digit portion of the dividend, this gives us the quotient $q=80809$.

In order for $8d<1000$, we need $d<125$. Only $d=124$ gives us a value of $a$ that has enough digits, so the calculation is

$$10020316 \div 124 =80809$$