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Math Help - How many pages?

  1. #1
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    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?
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  2. #2
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    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.
    Thanks from testtrail429
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