Rule of 9's. The digits in your answer will always be evenly divisible by 9; so the missing number will be 9 minus the number you give them. If you use 666, then rearranged it is still 666. You have to give them a zero answer (even tho you have to break one of their rules and circle zero). 9 minus 0 equals "9".
After all, I am the doctor of numbers ;)