17. Let $n$ be the smallest positive integer such that the sum of its digits is 2011 . How many digits does $n$ have?
17. Answer: 224 .
For smallest possible $n$, we need to have 9 as the digits of $n$ as many as poesible. So $n$ is the integer whose first digit is $2011-223 \times 9=4$ and followed by 2239 's.