Henry Ernest Dudeney/Puzzles and Curious Problems/83 - Three Different Digits/Solution/Proof 2

by : $83$

 * Three Different Digits

Proof
Here is the source code of a program in C which finds them all:

#include    int main {       for (int i = 100; i < 1000; i++) {           int a = i / 100; int b = (i / 10) % 10; int c = i % 10; if (a != b && b != c && c!= a && i % ((a + b + c)*(a + b + c)) == 0) printf("%d, ", i); }   }

Output: 162, 243, 324, 392, 405, 512, 605, 648, 810, 972,

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