Petya wrote a hundred-digit number $X$, in which there are no zeros. The fifty-digit number formed by the first fifty digits of the number $X$, Petya called the head of the number $X$. It turned out that the number $X$ is divisible by its head without a remainder. How many zeros are in the quotient? #
Let's append 50 zeros to the head of the number $X$ and subtract the resulting number from $X$. The result will be the "tail" of the number $X$, that is, the number formed by the last 50 digits of $X$. Since the difference between numbers that are divisible by the head is also divisible by the head, and the quotient cannot be a two-digit number: otherwise, there would be more digits in the tail than in the head, and they are equal. The quotient cannot be zero either, since there are no zeros in the representation of $X$. Therefore, the quotient of $X$ divided by the head consists of a one, 49 zeros, and a single-digit (non-zero) quotient of the tail divided by the head of the number $X$.

## Answer

49.