11: The loopiest puzzler [***]

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. // 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.

You can listen to 11: The loopiest puzzler [***] online on Radio and Podcast. Open the player on this page to stream the available audio.

11: The loopiest puzzler [***] is an episode from Wes Carroll's Puzzler by Wes Carroll.

This episode is 3:00 long.

This episode was published on May 22, 2016.

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