5.3. To number the pages of a book, a total of 1392 digits were used. How many pages are in this book?
Solution. The first nine pages will require 9 digits, and for the next 90 pages, 2 digits are needed for each page, which means 2 * 90 digits are required. Let the book have x pages, then the pages with three digits will be x - 99, and the digits on them will be 3 * (x - 99). We get the equation: $9 + 2 \cdot 90 + 3 \cdot (x - 99) = 1392$, the solution to which is $x = 500$.

Answer: 500.