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## Secret Santas II

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Fun: (2.64) Difficulty: (2.58) Category: Probability Submitted By: javaguru

A group of ten friends decide to exchange gifts as secret Santas. Each person writes his or her name on a piece of paper and puts it in a hat. Then each person randomly draws a name from the hat to determine who has him as his or her secret Santa. The secret Santa then makes a gift for the person whose name he drew.

When it's time to exchange presents, each person walks over to the person he made the gift for and holds his or her left hand in his right hand.

What is the probability that the 10 friends holding hands form a single continuous circle?

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 Posted by markmonnin on Jan 12, 2009 I think I understand, but I'm not sure. Are you assuming that the person can't draw his/her own name? I wonder if you get the same answer by taking 1/9 + 1/8 + 1/7 + ... Posted by markmonnin on Jan 12, 2009 Nevermind about that 1/9 + 1/8 + ... stuff. That wasn't well thought out. Posted by EntangledQuark on Mar 22, 2009 Very nice, elegant probability problem. While it was fairly easy to solve, I liked the way it turned out to be unexpectedly easier than it first seemed. Good job! Posted by Juanito on Jun 23, 2010 Easy and nice Posted by bigbanggoo on Jun 30, 2011 But what if the friends formed a triangle or a square or other polygon formations while holding hands instead? Wouldn't you have to calculate for the probability that they are actually forming a circle against other shapes while holding hands?