![11: The loopiest puzzler [***]](https://is1-ssl.mzstatic.com/image/thumb/Podcasts221/v4/de/96/d4/de96d4d4-1d23-6e15-9020-3987fbfa6228/mza_10060256328494827014.jpg/400x400bb.jpg "11: The loopiest puzzler [***]")
11: The loopiest puzzler [***]
Update: 2016-05-22
Description
I have four lengths of rope. I hold them so that you can see all eight ends, but you can’t tell which end connects to which other end. You pick a pair of ends, and I tie them together. We repeat -- you pick, I tie -- until we run out of ends.
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What’s the expected value of the number of loops you’ll have at the end? Or, in plain English, if we play this game a zillion times, what’s the average number of loops I’ll get per game? Note: the correct answer is not a whole number.
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What’s the expected value of the number of loops you’ll have at the end? Or, in plain English, if we play this game a zillion times, what’s the average number of loops I’ll get per game? Note: the correct answer is not a whole number.
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