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Search: id:A102263
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| A102263 |
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Denominators of probabilities in gift exchange problem with n people. |
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+0
2
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| 1, 4, 36, 144, 1800, 43200, 705600, 705600, 2116800, 127008000, 23051952000, 6638962176000, 280496151936000, 31415569016832000, 471233535252480000, 471233535252480000, 54474596675186688000, 3268475800511201280000
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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n friends organize a gift exchange. The n names are put into a hat and the first person draws one. If she picks her own name, then she returns it to the bag and draws again, repeating until she has a name that is not her own. Then the second person draws, again returning his own name if it is drawn. This continues down the line. What is the probability p(n) that when the n-th person draws, only her own name will be left in the bag?
I heard about the problem from Gary Thompson at Grove City College in PA.
As n increases, p(n) approaches 1/(n + log(n) + EulerGamma), where EulerGamma = .5772156649015... (the Euler-Mascheroni constant). - Jon E. Schoenfield (jonscho(AT)hiwaay.net), Sep 30 2006
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LINKS
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Math Forum at Drexel, A variant on the "Secret Santa"
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FORMULA
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See A102262 for formula for p(n).
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EXAMPLE
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p(2) through p(10) are 0, 1/4, 5/36, 19/144, 203/1800, 4343/43200, 63853/705600, 58129/705600, 160127/2116800.
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CROSSREFS
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Cf. A102262.
Sequence in context: A125756 A035287 A083223 this_sequence A103931 A068589 A120077
Adjacent sequences: A102260 A102261 A102262 this_sequence A102264 A102265 A102266
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KEYWORD
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nonn,frac
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AUTHOR
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Jerry Grossman (grossman(AT)oakland.edu), Feb 17 2005
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EXTENSIONS
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More terms from Jon E. Schoenfield (jonscho(AT)hiwaay.net), Sep 30 2006
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