Question

The page of a book starting with 1 and requires 3269 digits in all. How many page does the book have

Answer 1

The total number of pages in the book will be 1094.

Explanation

The page of a book is starting with 1 and requires 3269 digits in all.

From page 1 to 9, there are 9 pages with 1 digit numbers. So, the total digit= 9

From page 10 to 99, there are 90 pages with 2 digit numbers. So, the total digit= 90×2= 180

From page 100 to 999, there are 900 pages with 3 digit numbers. So, the total digit= 900×3= 2700

So, the total digits up to page 999 will be: $(9+180+2700)=2889$

As the book requires 3269 digits in all, so the number of remaining digits $=(3269-2889)=380$

This 380 digits will be for the pages with each of 4 digit.

So, the number of pages with 4 digits $=\frac{380}{4}=95$

Thus, the total number of pages in the book will be: $999+95=1094$

Answer 2

Total digit that are of single number lying between 1 and 9 = 9

Total of 2 digit number = 2 * 90 = 180

Total of 3 digit number = 3 * 900 = 2700

Total of 4 digit number = 3269 – (9 + 180 + 2700) = 380

Hence, total pages with 4 digit = 380/4 = 95

Hence, total pages = 999 + 95 = 1094