# Quotient by Digit Sum

Let $$S(N)$$ denote the digit sum of integer $$N$$. Let $$M$$ denote the maximum value of $$\frac {N} {S(N)}$$, where $$N$$ is a 3-digit number. How many 3-digit numbers $$N$$ satisfy $$\frac {N}{S(N)} = M$$?

Details and assumptions

The digit sum of an integer is the sum of all its digits. For example, the digit sum of $$N = 1123$$ is $$1+1+2+3=7$$.

The number $$12=012$$ is a 2-digit number, not a 3-digit number.

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