Digits Describing Digits

Since the digits describe how many there are of each digit, they must sum to 9 for a 9 digit number.

This means we can only have at most 1 digit which is 5/6/7/8, and if they are present they have to be the first digit since any other position would result in a sum greater than 9.

If we have none of these, the sum cannot reach 9 without the respective positions being non-zero which is invalid.

So there must be one of these digits present.

This produces a 1 in the respective position, so there must be a non-zero digit in the 1 position.

The 1 position cannot contain a 1 since that would make two of them, so it must be at least 2.

This places a 1 in the respective position (denoted as $n$ ).

These digits sum to $n\times1+n=2n$ , so the first digit is $9-2n\geq5$ .

This means $n\leq2$ but we already said $n\geq2$ so $n=2$ .

So the answer is $\boxed{521001000}$