Henry Ernest Dudeney/Puzzles and Curious Problems/88 - Digital Progression

Puzzles and Curious Problems by Henry Ernest Dudeney: $88$

Digital Progression

If you arrange the nine digits in three numbers thus, $147$, $258$, $369$,

they have a common difference of $111$ and are therefore in arithmetic progression.

Can you find $4$ ways of rearranging the $9$ digits so that in each case the number shall have a common difference,

and the middle number be in every case the same?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $88$. -- Digital Progression
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $125$. Digital Progression