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

by : $83$

 * Three Different Digits
 * Find all $3$-digit numbers with distinct digits that are divisible by the square of the sum of those digits.


 * For example, $112$ is such that $\paren {1 + 1 + 2}^2 = 16$, and $16$ is a divisor of $112$.
 * However, the digits of $112$ are not all different, so it does not count.