## Task 4 - 140614

Someone writes 3 * 6 * 5 and then wants to replace the asterisks * with digits to form a five-digit number that is divisible by 75.

Determine all five-digit numbers that are divisible by 75 and can be formed under these conditions!
A number divisible by 75 ends in $0, 25, 50$ or 75, meaning the second-to-last digit is a 2 or 7. Since 75 is also divisible by 3, the number in question must also be divisible by 3. Its digit sum is $q=3+a+6+b+5=14+a+b$ with $b=2$ or $b=7$.

If $b=2$, the digit sum is $q=16+a$, meaning $a$ can be 2, 5, or 8.

If $b=7$, the digit sum is $q=21+a$, meaning $a$ can be $0, 3, 6$ or 9.

Thus, the five-digit number can be

$$
32625, \quad 35625, \quad 38625, \quad 30675, \quad 33675, \quad 36675, \quad 39675
$$