Math

How many numbers between 9 and 100 exist such that the product of the digits is treaters than the actual number?

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  1. I will assume a typo, and "treaters" is "greater"

    let the unit digit of the number be x
    let the tens digit of the number by y

    so the number is 10y+x
    and the product of the digits is xy

    when is xy > 10y+x
    xy - 10y > x
    y(x-10) > x
    y > x/(x-10)
    but x can only be a positive integer from 0 to 9
    so x-10 will be always negative
    and x/(x-10) can never be a positive integer.

    So there are no such numbers

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