# One Half as Pandigital Fraction

## Theorem

There are $12$ ways $\dfrac 1 2$ can be expressed as a pandigital fraction:

$\dfrac 1 2 = \dfrac {6729} {13 \, 458}$
$\dfrac 1 2 = \dfrac {6792} {13 \, 584}$
$\dfrac 1 2 = \dfrac {6927} {13 \, 854}$
$\dfrac 1 2 = \dfrac {7269} {14 \, 538}$
$\dfrac 1 2 = \dfrac {7293} {14 \, 586}$
$\dfrac 1 2 = \dfrac {7329} {14 \, 658}$
$\dfrac 1 2 = \dfrac {7692} {15 \, 384}$
$\dfrac 1 2 = \dfrac {7923} {15 \, 846}$
$\dfrac 1 2 = \dfrac {7932} {15 \, 864}$
$\dfrac 1 2 = \dfrac {9267} {18 \, 534}$
$\dfrac 1 2 = \dfrac {9273} {18 \, 546}$
$\dfrac 1 2 = \dfrac {9327} {18 \, 654}$

## Proof

Can be verified by brute force.

## Historical Note

According to David Wells in his $1986$ work Curious and Interesting Numbers, this result appears 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.