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 3-digit number. How many 3-digit numbers N satisfy N/S(N)=M?

Question

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.

Answer 1

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).