294.Loops From a Hundred Noodles
★★★expected valueTower Research Capital
A bowl holds 100 noodles, giving 200 free ends. You repeatedly pick two free ends at random and tie them together, until no free ends remain. What is the expected number of loops formed?
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Count loops as they are created. At each tie, a loop appears exactly when you happen to join a piece to itself — and that probability depends only on how many ends are left.
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