Question 39
Let $S(n)$ denote the sum of the digits of the natural number $n$. For example: $n = 2456$, $S(n) = S(2456) = 2+4+5+6=16$, $S(S(n)) = S(S(2456)) = S(16)=1+6=7$. Is there a natural number $n$ for which $n + S(n) + S(S(n)) = 2011$.
Math Olympiad Vault · MathNet 2011