For instance: Let the number is $123$, then sum of all permutation of $123$ is $1332$
2.If $A=[0,1,2,........,9]$ then we have a $n$ digit number formed by using the digits from $A$. The sum of all the possible numbers is $S$. Then prove that, $S$ has $2n$ digit for all $n \in \mathbb{N}$ and $n\geq 2$
Note that here you're free for repetition. But you can't use zero for the first digit.
3. Assume that some of the numbers are wiped out form set $A$. Then what is the generalization for finding S and the number of digit of $S$.
N.B:This problems are a little manipulation of a problem from MILON da. Thanks to MILON da.
