In detail

How many pages does the book have?

How many pages does the book have?

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.