A book uses exactly 264 digits for its page numbers Each page is numbered and the first page is 1 which is obviously 1 digit How many pages does the book have?

Answer 1

Pages 1 - 9 each have one digit, and so in total they use 9. Pages 10 - 99 each have two digits. There are 90 pages there, so we have now used 9 + (90 x 2) = 189 digits. Our book uses 264 - 189 = 75 digits more than this. That equates to 25 pages with three digits: pages 100 to 124 inclusive. So the book has 124 pages. Pages 1 - 9: 9 digits Pages 10 - 99: 180 digits. Pages 100 - 124: 75 digits. Total: 264 digits.