In a four-digit number, the product of the thousands digit and the units digit is zero, while their difference is 7. The product of the middle digits is 18. The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is _____________.

The product of the thousands digit and the unit digit is zero; thus, the unit digit will be 0 (because if the thousands digit is 0, then it won't be a four-digit number). Also, their difference is 7, thus the thousands digit is 7.

Number = 7ab0

The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit => a = b + 7

The product of the middle digits is 18 

=> ab = 18

=> b(b+7) = 18

=> b = 2 and a = 9

Therefore, the number is 7920.