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): $0 \cdotp 5$