Solution:

From lines (4) and (5), we find that the divisor, when multiplied by 9, gives a three-digit number. This means that the divisor can be no greater than 111.

Notice line (3). The divisor, when multiplied by a certain number, gives a three-digit number. However, this three-digit number is not a random one. This is because if we observe lines (2) and (4) as well, we will see that when this three-digit number is subtracted from a four-digit number, a one-digit number results. (They are the squares in red.) So this three-digit number is at least 1000 - 9 = 991. This means that the divisor has a multiple between 991 and 999 inclusive.

However, none of the numbers 100 to 110 has a factor between 991 and 999. So the divisor must be 111. (111 has a multiple 999). Thus the first digit of the quotient is 9. The second digit of the quotient is clearly 0. So the quotient is 909, and the dividend is 909 ’ 111 = 100899. The rest can be worked out by actually carrying out the division.

Thus we have the solution: