Problem 2. To number the pages of a textbook, 411 digits are needed. How many pages does the textbook have?
Solution. The book has 173 pages. For the single-digit pages, 9 digits are used, and for the double-digit pages, $90 \cdot 2=180$ digits are used. This means there are $411-189=222$ digits left, which is $222: 3=74$ pages that can be numbered with the remaining digits. Therefore, the book has $9+90+74=173$ pages.