Fomin S.B.

A natural number $n$ is written in the decimal system. It is known that if any digit is included in this representation, then $n$ is divisible by this digit (0 does not appear in the representation). What is the maximum number of different digits that this representation can contain?
If the digit 5 is included in the number, then the number must end in 5. Thus, it is odd and, consequently, contains only odd digits. Therefore, it cannot have more than five digits. If 5 does not appear in the decimal representation of the number, then it can include all the other 8 digits. Here is an example: 1471963248. This number is divisible by $1,2,3,4,6,7,8,9$.

## Answer

8 digits.