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?
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): .$\displaystyle 9$ 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.