One Half as Pandigital Fraction
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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.
Also see
- One Third as Pandigital Fraction
- One Quarter as Pandigital Fraction
- One Fifth as Pandigital Fraction
- One Sixth as Pandigital Fraction
- One Seventh 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 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.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $0 \cdotp 5$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $0 \cdotp 5$