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

Puzzles and Curious Problems by Henry Ernest Dudeney: $105$

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.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $105$. -- Equal Fractions
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $133$. Equal Fractions