Minimum Digit Sum Fraction

Algebra Level 3

Let \(S(N) \) denote the digit sum of the integer \(N\). As \(N\) ranges over all 3-digit positive numbers, what value of \(N\) would give the minimum of \(M = \frac{N}{S(N)}\)?

Details and assumptions

The number \(12=012\) is a 2-digit number, not a 3-digit number.

The digit sum of a number is the sum of all its digits. For example the digit sum of 1123 is \(1 + 1 + 2 + 3 = 7\).


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