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?

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- Jan 30th 2013, 04:33 PMtesttrail429How 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?

- Jan 30th 2013, 04:52 PMSorobanRe: How many pages?
Hello, testtrail429!

There is no formula for this problem.

We must "talk" our way through it.

Quote:

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): .$\displaystyle 9$ digits.

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

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

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

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

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

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