Loops from tying noodles
A bowl holds noodles, each with two ends ( ends total). You repeatedly pick two ends uniformly at random and tie them together, until no free ends remain. On average, how many closed loops form? Round to the nearest whole number.
Show hints (2)+
- With strands, tying a chosen end closes a loop with probability (the strand's own other end).
- Sum by linearity: .
Answer
Reveal answer →Final answer
3
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