math

A person writing a book numbered the pages consecutively starting with 1 and had written 4553 digits. how many pages had she numbered?

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  1. single digits 1-9 or 9 --- 9 digits used
    double digits 10-99 or 90
    using 2 digits each gives us --- 180 digits used for doubles
    triple digits 100 - 999 -- 900
    using 3 digits each , 900x3 = 2700 used for triples

    number of digits used for 4 digits numbers
    = 4553 - 9 - 180 - 2700 = 1664
    number of pages using 4 digits = 1664/4 = 416

    she had numbered 1415 pages

    (it is not 1416,
    since 1000 is the first of the 4 digits
    1001 is the 2nd of the 4 digits
    .
    .
    1415 is 416th of the 4 digits numbers)

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