Answer to Question #89552 in Combinatorics | Number Theory for Aravind

Question

A printer numbers the pages of a book starting with one and uses 3189 digits in all. How many pages does the book have?

Answer 1

Number of digits in 1-digit page numbers (from 1 to 9)=1×9=9

Number of digits in 2-digit page numbers (from 10 to 99)=2×90=180

Number of digits in 3-digit page numbers (from 101 to 999)=3×900=2700

Number of digits in 4-digit page numbers=3189-(9+180+2700)=3189–2889=300

Therefore, number of pages with 4-digit page numbers=(300/4)=75

Hence, total number of pages in the book=(999+75)=1074

The book has 1074 pages.