12. Let $A, B, C$ be positive integers such that the number $1212017 A B C$ is divisible by 45 . Find the difference between the largest and the smallest possible values of the two-digit number $A B$.
Answer: 85
Solution: Since the number is divisible by 45 , it must be divisible by both 9 and 5 . If $C$ is 0 , then $A$ and $B$ must have a sum of either 4 or 13 . If $C$ is 5 , then $A$ and $B$ can either have a sum of 8 or 17. Based from these, the largest and smallest values of $A B$ are 98 and 13 , respectively, which have a difference of 85 .