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

Puzzles and Curious Problems by Henry Ernest Dudeney: $83$

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $83$. -- Three Different Digits
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $122$. Three Different Digits