Henry Ernest Dudeney/Modern Puzzles/51 - An Exceptional Number

Modern Puzzles by Henry Ernest Dudeney: $51$

An Exceptional Number

A number is formed of $5$ successive digits (not necessarily in regular order)

so that the number formed by the first $2$ multiplied by the central digit will produce the number expressed by the last $2$.

Thus if it were $1 \, 2 \,8 \, 9 \, 6$, then $12$ multiplied by $9$ produces $96$.

But, unfortunately, $1, 2, 6, 8, 9$ are not successive numbers, so it will not do.

Variant

A number is formed of $6$ successive digits (not necessarily in regular order)

so that the number formed by the first $2$ multiplied by the $3$rd digit will produce the number expressed by the last $3$.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $51$. -- An Exceptional Number
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $102$. An Exceptional Number