To number the pages of a book, a total of 2989 digits have been used. Knowing that the first page of the book is numbered 1,

**What is the number of the last page of the book?**

#### Solution

Pages 1 to 9 have only one digit each, so we will need 9 digits in total to number them. Pages 10 through 99 (90 in total) have two digits so we will need 90 * 2 = 180 digits in total to number them. Pages 100 through 999 (900 in total) need 3 digits each, so we need 2,700 digits in total. Adding we have 2889 digits used so we have 100 digits left to express the numbered pages with 4 digits that in total will be 100/4 = 25 pages, from 1000 to 1024 so **the last page of the book will be number 1024**.