Henry Ernest Dudeney/Puzzles and Curious Problems/105 - Equal Fractions

by : $105$

 * Equal Fractions
 * Can you construct three ordinary vulgar fractions
 * (say, $\tfrac 1 2$, $\tfrac 1 3$, or $\tfrac 1 4$, or anything up to $\tfrac 1 9$ inclusive)
 * all of the same value, using in every group all the nine digits once, and once only?


 * The fractions may be formed in one of the following ways:
 * $\dfrac a b = \dfrac c d = \dfrac {e f} {g h j}$, or $\dfrac a b = \dfrac c {d e} = \dfrac {f g} {h j}$.


 * We have only found five cases, but the fifth contains a simple little trick that may escape the reader.