One Seventh as Pandigital Fraction

Theorem

There are $7$ ways $\dfrac 1 7$ can be expressed as a pandigital fraction:

$\dfrac 1 7 = \dfrac {2394} {16 \, 758}$
$\dfrac 1 7 = \dfrac {2637} {18 \, 459}$
$\dfrac 1 7 = \dfrac {4527} {31 \, 689}$
$\dfrac 1 7 = \dfrac {5274} {36 \, 918}$
$\dfrac 1 7 = \dfrac {5418} {37 \, 926}$
$\dfrac 1 7 = \dfrac {5976} {41 \, 832}$
$\dfrac 1 7 = \dfrac {7614} {53 \, 298}$

Proof

Can be verified by brute force.

Historical Note

According to David Wells in his $1986$ work Curious and Interesting Numbers, this result may have appeared in an article by Mitchell J. Friedman in Volume $8$ of Scripta Mathematica, but it is proving difficult to find an archived copy to consult directly.