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Topic: Making Fractions (Read 244 times) |
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otter
Junior Member
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Posts: 142
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Making Fractions
« on: May 20th, 2003, 9:15pm » |
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If you take all of the non-zero digits and place them as follows:
6729
13458
you will have a fraction equal in value to one-half. Can you rearrange the nine non-zero digits similarly so as to form fractions exactly equal to one-third, one-fourth, one-fifth, one-sixth, one-seventh, one-eighth and one-ninth?
You may use each digit only once for each fraction.
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We shall not cease from exploration. And the end of all our exploring will be to arrive where we started
and know the place for the first time.
T.S. Eliot
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BNC
Uberpuzzler
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Re: Making Fractions
« Reply #1 on: May 21st, 2003, 12:23am » |
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Wow, that's an old one.
A followup question:
Each of the fractions may be achieved using more that a single way. What is the fraction with the maximal number of possibilities?
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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Leo Broukhis
Senior Riddler
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Re: Making Fractions
« Reply #2 on: May 21st, 2003, 6:46am » |
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A 20-line program in C prints all 187 solutions of
<a combination of 4 digits> / <a combination of 5 remaining digits> = 1 / <integer>
in less than a second, starting with 12 solutions for one-half and ending with
1452 / 98736 = 1 / 68
The possible ratios include, in addition to 2 to 9: 12 to 19, 22-24, 26-29, 32, 35, 37, 38, 43, 44, 46, 52, 53, 59, 62, 66, 68
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| « Last Edit: May 21st, 2003, 6:47am by Leo Broukhis » |
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