# Math Help - How many pages?

1. ## How many pages?

The pages of a book are numbered, beginning with page 1. If all of the pages in the book are considered, there are a total of 2,989 individual digits needed to print the page numbers. How many pages does the book contain?

2. ## Re: How many pages?

Hello, testtrail429!

There is no formula for this problem.
We must "talk" our way through it.

The pages of a book are numbered, beginning with page 1.
There is a total of 2,989 individual digits needed to print the all page numbers.
How many pages does the book contain?

There are 9 one-digit numbers (1 to 9): . $9$ digits.

There are 90 two-digit numbers (10 to 99): . $2\times 90 \,=\,180$ digits.

There are 900 three-digit numbers (100 to 999): . $3\times 900 \,=\,2700$ digits.

We have accounted for: $9 + 180 + 2700 \,=\,2889$ digits.

There are: . $2989 - 2889 \,=\,100$ digits left.

They will be used by the first 25 four-digit numbers (from 1000 to 1024).

Therefore, the book contains $\color{blue}{1024}$ pages.