Henry Ernest Dudeney/Modern Puzzles/67 - A Digital Difficulty

Modern Puzzles by Henry Ernest Dudeney: $67$

A Digital Difficulty

Arrange the $10$ digits, $1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9 \ 0$, in such order that they shall form a number

that may be divided by every number from $2$ to $18$ without in any case a remainder.

As an example, if I arrange them thus, $1 \ 2 \ 7 \ 4 \ 9 \ 5 \ 3 \ 6 \ 8 \ 0$, this number can be divided by $2$, $3$, $4$, $5$ and so on up to $16$, without any remainder,

but it breaks down at $17$.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $67$. -- A Digital Difficulty
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $118$. A Digital Difficulty