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

by : $52$

 * 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.