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    Primary 5 math problem sum 2

    Joshua counted the number of digits of all the page numbers in an encyclopedia. He found that a total of 1359 digits were used.
    How many pages were there in the book?
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    Quote Originally Posted by mytan1963 View Post
    Joshua counted the number of digits of all the page numbers in an encyclopedia. He found that a total of 1359 digits were used.
    How many pages were there in the book?
    The way I'd do this would be to split it up into totals for the 1-digit pages, then the 2-digit pages, then the 3-digit pages etc.

    So there are 9 1-digit pages: that's 9.

    Then there are 90 2-digit pages: that's 90 x 2 = 180.

    Then there are a possible 900 3-digit pages: that's 900 x 3 = 2700.

    Whoops, that's way over. That means there's definitely less than 1000 pages here.

    So you need to find a number of 3-digit pages that make the total you need. Call that number n

    So you have 9 + 180 + 3n = 1359.

    That looks quite easy. Don't forget n is the number of 3-digit pages - you have to add to that the number of 1 and 2 digit pages when you've finished.
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