118. Threes and sevens. What is the smallest number that is written using only the digits 3 and 7 and that both the number itself and the sum of its digits are divisible by 3 and 7? For example, 7733733 is divisible by 3 and 7 without a remainder, but the sum of its digits (33) is divisible by 3, not by 7, so it cannot serve as a solution to the problem.
118. The smallest possible number is 3333377733. It is divisible by 3 and 7, and the sum of its digits (42) has the same property. The number must contain at least 3 sevens and 7 threes, with the sevens being moved as far to the right as possible.