Question:
A textbook has 1,000 pages.  How many of the pages have page numbers whose digits add up to exactly 4?

Answer:
There are only a few ways to make one, two, and three digit numbers add up to $4$.  The only one-digit number whose sum is $4$ is $4$ itself.  Continuing with two-digit numbers, we note that the digits must be $4$ and $0$, $1$ and $3$, or $2$ and $2$.  This means that $13$, $22$, $31$, and $40$ are the only two-digit numbers whose digits sum to 4.  For the three-digit numbers, we organize the work in a table.

\begin{tabular}{|c|c|c|}\hline
Possible Digits&Possible Numbers&Total Possibilities\\\hline
4,0,0&400&1\\\hline
3,1,0&103, 130, 301, 310&4\\\hline
2,2,0&202, 220&2\\\hline
2,1,1&112, 121, 211&3\\\hline
\end{tabular}Adding up the last column, we see that there are $10$ three-digits numbers whose digits add up to $4$.  Adding those to the possible one-and-two digit numbers, we get $\boxed{15}$ pages in the textbook which have digits that add up to $4$.