An Interesting Problem?

We can see that $1000$ is $3E8$ in hexadecimal. Using this, we can move forward by constructing numbers that consist of only numeric digits in hexadecimal. The first digit could be $0,1,2$ or $3$ , and the second two could be any digits from $0 \Longrightarrow 9$ , giving us a total of $4 \times 10 \times10 = 400$ combinations. However, this number of combinations also includes $000$ , so the total number of combinations must be subtracted by $1$ . Thus, there are $399$ valid $n$ corresponding to those $399$ positive integers less than $1000$ that consist of only numeric digits. Since we are asked to find the sum of the digits, we can add ${[399]} \Rightarrow 3 + 9 + 9 = 3 + 18 = \boxed{21}$ .