Braingle: 'Secret Santas II' Brain Teaser

Secret Santas II

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

Puzzle ID:	#43900
Fun:	(2.63)
Difficulty:	(2.59)
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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Comments

markmonnin 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 + ...
markmonnin Jan 12, 2009	Nevermind about that 1/9 + 1/8 + ... stuff. That wasn't well thought out.
EntangledQuark 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!
Juanito Jun 23, 2010	Easy and nice
bigbanggoo 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?