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        riddles >> medium >> expected number of hoops and loops
        
(Message started by: inexorable on Jan 7th, 2012, 6:26pm)
Title: expected number of hoops and loops
Post by inexorable on Jan 7th, 2012, 6:26pm
First, Happy New Year Everyone!

A bowl of spaghetti contains n strands. Thor picks two ends at random and joins them together. He does this until no ends remain.

What is the expected average length of the loops? (length measured as number of  strands in a loop)

What is the expected number of k-hoops? ( a k-hoop is a loop made from k strands)
Title: Re: expected number of hoops and loops
Post by SMQ on Jan 8th, 2012, 5:44am
Related to Rope Loops (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=display;num=1184787474), I believe.

--SMQ


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