Find the difference between the greatest and the smallest 4-digit numbers formed by the digits 0, 3, 6, 9

The given digits are 0, 3, 6 and 9, and each digit is used only once.

For the greatest 4-digit number, arrange the digits in descending order: 9, 6, 3, 0.

Greatest 4-digit number = 9,630.

For the smallest 4-digit number, the thousand's place cannot be 0. So, place the smallest non-zero digit (3) at the thousand's place, then arrange the remaining digits (0, 6, 9) in ascending order.

Smallest 4-digit number = 3,069.

Difference = 9,630 - 3,069

= 6,561

Hence, the difference between the greatest and the smallest 4-digit numbers is 6,561.