# One Eighth as Pandigital Fraction

## Theorem

There are $46$ ways $\dfrac 1 8$ can be expressed as a pandigital fraction:

$\dfrac 1 8 = \dfrac {3187} {25496}$
$\dfrac 1 8 = \dfrac {4589} {36712}$
$\dfrac 1 8 = \dfrac {4591} {36728}$
$\dfrac 1 8 = \dfrac {4689} {37512}$
$\dfrac 1 8 = \dfrac {4691} {37528}$
$\dfrac 1 8 = \dfrac {4769} {38152}$
$\dfrac 1 8 = \dfrac {5237} {41896}$
$\dfrac 1 8 = \dfrac {5371} {42968}$
$\dfrac 1 8 = \dfrac {5789} {46312}$
$\dfrac 1 8 = \dfrac {5791} {46328}$
$\dfrac 1 8 = \dfrac {5839} {46712}$
$\dfrac 1 8 = \dfrac {5892} {47136}$
$\dfrac 1 8 = \dfrac {5916} {47328}$
$\dfrac 1 8 = \dfrac {5921} {47368}$
$\dfrac 1 8 = \dfrac {6479} {51832}$
$\dfrac 1 8 = \dfrac {6741} {53928}$
$\dfrac 1 8 = \dfrac {6789} {54312}$
$\dfrac 1 8 = \dfrac {6791} {54328}$
$\dfrac 1 8 = \dfrac {6839} {54712}$
$\dfrac 1 8 = \dfrac {7123} {56984}$
$\dfrac 1 8 = \dfrac {7312} {58496}$
$\dfrac 1 8 = \dfrac {7364} {58912}$
$\dfrac 1 8 = \dfrac {7416} {59328}$
$\dfrac 1 8 = \dfrac {7421} {59368}$
$\dfrac 1 8 = \dfrac {7894} {63152}$
$\dfrac 1 8 = \dfrac {7941} {63528}$
$\dfrac 1 8 = \dfrac {8174} {65392}$
$\dfrac 1 8 = \dfrac {8179} {65432}$
$\dfrac 1 8 = \dfrac {8394} {67152}$
$\dfrac 1 8 = \dfrac {8419} {67352}$
$\dfrac 1 8 = \dfrac {8439} {67512}$
$\dfrac 1 8 = \dfrac {8932} {71456}$
$\dfrac 1 8 = \dfrac {8942} {71536}$
$\dfrac 1 8 = \dfrac {8953} {71624}$
$\dfrac 1 8 = \dfrac {8954} {71632}$
$\dfrac 1 8 = \dfrac {9156} {73248}$
$\dfrac 1 8 = \dfrac {9158} {73264}$
$\dfrac 1 8 = \dfrac {9182} {73456}$
$\dfrac 1 8 = \dfrac {9316} {74528}$
$\dfrac 1 8 = \dfrac {9321} {74568}$
$\dfrac 1 8 = \dfrac {9352} {74816}$
$\dfrac 1 8 = \dfrac {9416} {75328}$
$\dfrac 1 8 = \dfrac {9421} {75368}$
$\dfrac 1 8 = \dfrac {9523} {76184}$
$\dfrac 1 8 = \dfrac {9531} {76248}$
$\dfrac 1 8 = \dfrac {9541} {76328}$

## Proof

Can be verified by brute force.