Clearing the Tightrope
IMC TradingWincentSIG
Five hundred point-sized beetles land at independent, uniformly random spots on a taut 1-foot wire. Each one immediately flips a fair coin to pick a direction and crawls at 1 foot per minute. Whenever two beetles meet head-on, both instantly turn around and continue crawling; a beetle that reaches either end of the wire drops off. How long, in expectation, until the wire is completely clear?
Answer
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