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