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Topic: a gift exchange
Replies: 6   Last Post: Aug 10, 2013 11:20 PM

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Jerry Grossman

Posts: 27
Registered: 12/6/04
Re: a gift exchange
Posted: Nov 24, 2004 7:49 AM
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This problem has been floating around for a few years. I heard
it from Gary Thompson, Grove City College (Pennsylvania).
I don't think anyone has the general solution (with n people).
You can use a computer to brute force your way to the answer
for small values of n. In particular, the answer for n=10 is
160127/2116800, which is about 0.075645786.

If anyone has any information about solutions, I'd very much
like to hear about it.

Jerry Grossman
Oakland University

---- Original message ----
>Date: 23 Nov 04 20:51:41 -0500 (EST)
>From: John <sternitj@uwplatt.edu>
>Subject: a gift exchange
>To: discretemath@mathforum.org
>
>Ten friends organize a gift exchange. The ten names are put in a hat,
>and the first person draws one. If they pick their own name, they
>return it to the bag and draw again, until they have a name that is
>not their own. Then the second person draws, again returning their
>own name if they draw it. This continues down the line. What is the
>probability that when the 10th person draws, only their own name will
>be left in the bag?
>
>Any help!!!
--
Jerrold W. Grossman, Professor
Department of Mathematics and Statistics
346 SEB
Oakland University
Rochester, MI 48309-4485
248-370-3443 (voice)
248-370-4184 (fax)
grossman@oakland.edu
<a href="http://personalwebs.oakland.edu/~grossman/">http://personalwebs.oakland.edu/~grossman/</a>




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