number theory - Divisibility by 7 or 3

I read a question on mathematics.I have not been able to figure out the answer.

the question is

given a set $Q=\{1,2,3,4,5,6,7\}$ such that I can have a subset $L$ from this set $Q$. I have been given a number string $Y$ in such a way that I know its starting digit and the end digit.

Now the rest of the digits from second digit to the last but one digit can be have any numbers of digits from the subset $L$.

Now the question how can i decide whether $Y$ can be made divisible by $3$ or $7$.