# One Seventh as Pandigital Fraction

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## 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.

## Also see

- One Half as Pandigital Fraction
- One Third as Pandigital Fraction
- One Quarter as Pandigital Fraction
- One Fifth as Pandigital Fraction
- One Sixth as Pandigital Fraction
- One Eighth as Pandigital Fraction
- One Ninth as Pandigital Fraction

## 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.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $0 \cdotp 5$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $0 \cdotp 5$