Henry Ernest Dudeney/536 Puzzles & Curious Problems/102 - An Exceptional Number/Solution

536 Puzzles & Curious Problems by Henry Ernest Dudeney: $102$

An Exceptional Number

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 $3$.

Solution

We have:

$9 \ 4 \ 7 \ 6 \ 5 \ 8$

as:

$94 \times 7 = 658$

Historical Note

Martin Gardner includes this variant on $51$ - An Exceptional Number from Dudeney's Modern Puzzles as an aside in the Answers section of his $1968$ repackaging 536 Puzzles & Curious Problems.

He attributes its discovery to Victor Meally.

Sources

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