11: The loopiest puzzler [***]
Wes Carroll's Puzzler
English - May 22, 2016 04:00 - 3 minutes - 1.42 MB - ★★★★★ - 2 ratingsLeisure Education Courses math puzzles puzzle puzzler amc riddles problem-solving math contest math competition Homepage Download Apple Podcasts Google Podcasts Overcast Castro Pocket Casts RSS feed
Previous Episode: 10: Eight's too many [**]
Next Episode: 12: One light switch [****]
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.