Henry Ernest Dudeney/Modern Puzzles/52 - The Five Cards

Modern Puzzles by Henry Ernest Dudeney: $52$

The Five Cards

I have $5$ cards bearing the figures $1$, $3$, $5$, $7$ and $9$.

How can I arrange them in a row so that the number formed by the $1$st pair multipied by the number formed with the last pair,

with the central number subtracted,

will produce a number composed of repetitions of one figure?

$\boxed 3 \boxed 1 \ \boxed 5 \ \boxed 7 \boxed 9$

Thus, in the example I have shown, $31$ multiplied by $79$ and $5$ subtracted will produce $2444$,

which would have been all right if that $2$ had happened to be another $4$.

Of course, there must be $2$ solutions, for the pairs are clearly interchangeable.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $52$. -- The Five Cards
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $103$. The Five Cards