Algebra
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Let S(N) denote the digit sum of the integer N. Let M denote the maximum value of N/S(N), where N is a 3digit number. How many 3digit numbers N satisfy N/S(N)=M?
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.

9. The maximum value of N/S(N) is 100, and for N = 100, 200, 300, 400, ..., 900, we get the desired value of N/S(N).
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