Today in math class, a number puzzle arose where you would have to find a 10 digit number, where each digit describes the number of other digits in the number, for example:
$$\text{0 1 2 3 4 5 6 7 8 9}$$
$$\text{6 2 1 0 0 0 1 0 0 0}$$
$\textit{The top row being digit number $n$, and the bottom row being the $10$ digit number.}$
You can see that since there are six zeros in the $10$ digit number, there is a $6$ in the $0$'s column. And since there are two $1$'s, there is a $2$ in the $1$'s column and so on.
So, my question would be: Are there any more solutions to this puzzle? And if not, how could you prove this?