# One Fifth as Pandigital Fraction

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## Theorem

There are $12$ ways $\dfrac 1 5$ can be expressed as a pandigital fraction:

- $\dfrac 1 5 = \dfrac {2697} {13485}$

- $\dfrac 1 5 = \dfrac {2769} {13845}$

- $\dfrac 1 5 = \dfrac {2937} {14685}$

- $\dfrac 1 5 = \dfrac {2967} {14835}$

- $\dfrac 1 5 = \dfrac {2973} {14865}$

- $\dfrac 1 5 = \dfrac {3297} {16485}$

- $\dfrac 1 5 = \dfrac {3729} {18645}$

- $\dfrac 1 5 = \dfrac {6297} {31485}$

- $\dfrac 1 5 = \dfrac {7629} {38145}$

- $\dfrac 1 5 = \dfrac {9237} {46185}$

- $\dfrac 1 5 = \dfrac {9627} {48135}$

- $\dfrac 1 5 = \dfrac {9723} {48615}$

## Proof

Can be verified by brute force.