$9 \cdot 13$ In decimal notation, what is the smallest natural number whose digits are 0 or 1 and which is divisible by 225?
(China Junior High School Mathematics League, 1989)
[Solution] Notice that $225=9 \cdot 25$, and 9 and 25 are coprime. Therefore, the number we are looking for should be divisible by both 9 and 25.
If this number is divisible by 25, then its last two digits must both be 0, i.e., they must be 00.
If this number is divisible by 9, then the sum of its digits must be divisible by 9. To make it as small as possible, it should consist of 9 ones.
Thus, the smallest natural number that meets the requirements of the problem is
$$
11111111100 .
$$