Question 13
Let $S(n)$ be the sum of all digits in the decimal representation of $n \in \mathbb{N}$. Do there exist integers $n$ such that
$$
a)\quad n - S(n) = 3 \cdot 2010? \qquad b)\quad n - S(n) = 3 \cdot 2011?
$$
(I. Gorodnin)
$$
a)\quad n - S(n) = 3 \cdot 2010? \qquad b)\quad n - S(n) = 3 \cdot 2011?
$$
(I. Gorodnin)