Book Pages

For the purposes of this problem, we will assume that every page in an book is numbered sequentially, and that the first page is numbered 1. How many digits would you need to use to number the pages of a 10 page book? Pages 1 to 9 would require 1 digit each (total 9), and page 10 would require 2 digits. This makes 11 digits. Similarly, a book of 34 pages would require 59 digits. Can we work backwa