Question

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

Answer 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