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

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 $2$.

Solution

We have:

$1 \, 3 \, 4 \, 5 \, 2$

as:

$13 \times 4 = 52$

It remains to be shown that there are no more.

This could be implemented by means of a computer search.

Sources

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