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Search: id:A121228
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| A121228 |
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Number of ways to write the numbers 1 through 3n on the faces of three n-sided dice, so that the 1st die beats the 2nd with probability > 1/2, the 2nd beats the 3rd with probability > 1/2 and the 3rd beats the 1st with probability > 1/2. |
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+0
1
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OFFSET
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1,3
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REFERENCES
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M. Gardner, "Mathematical Games: The Paradox of the Nontransitive Dice and the Elusive Principle of Indifference." Sci. Amer. 223, 110-114, Dec. 1970.
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LINKS
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Lee J. Stemkoski, Nontransitive Dice
Eric Weisstein's World of Mathematics, Efron's Dice.
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EXAMPLE
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a(3)=5:
Set 1:
Die 1: 1 5 9
Die 2: 3 4 8
Die 3: 2 6 7
Set 2:
Die 1: 1 7 8
Die 2: 4 5 6
Die 3: 2 3 9
Set 3:
Die 1: 1 7 8
Die 2: 3 5 6
Die 3: 2 4 9
Set 4:
Die 1: 1 6 8
Die 2: 4 5 7
Die 3: 2 3 9
Set 5:
Die 1: 1 6 8
Die 2: 3 5 7
Die 3: 2 4 9
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CROSSREFS
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Sequence in context: A009157 A153374 A012032 this_sequence A012173 A009143 A127317
Adjacent sequences: A121225 A121226 A121227 this_sequence A121229 A121230 A121231
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KEYWORD
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more,nonn
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AUTHOR
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Mikhail Dvorkin (dvorkin_m(AT)yahoo.com), Dec 11 2006
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EXTENSIONS
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a(1) corrected by Jon Schoenfield (jonscho(AT)hiwaay.net), May 19 2007
a(6) and a(7) from Jon Schoenfield (jonscho(AT)hiwaay.net), May 19 2007
a(8) from Jon E. Schoenfield (jonscho(AT)hiwaay.net), May 23 2007
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