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Omni-MATH / There is a unit circle that starts out painted white. Every second, you choose…

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problem

There is a unit circle that starts out painted white. Every second, you choose uniformly at random an arc of arclength 1 of the circle and paint it a new color. You use a new color each time, and new paint covers up old paint. Let cnc_{n} be the expected number of colors visible after nn seconds. Compute limn→∞cn\lim _{n \rightarrow \infty} c_{n}.
Plain-text mathematical notation (without MathML)
There is a unit circle that starts out painted white. Every second, you choose uniformly at random an arc of arclength 1 of the circle and paint it a new color. You use a new color each time, and new paint covers up old paint. Let c_(n) be the expected number of colors visible after n seconds. Compute lim_(n→∞)c_(n).
Original LaTeX notation
There is a unit circle that starts out painted white. Every second, you choose uniformly at random an arc of arclength 1 of the circle and paint it a new color. You use a new color each time, and new paint covers up old paint. Let $c_{n}$ be the expected number of colors visible after $n$ seconds. Compute $\lim _{n \rightarrow \infty} c_{n}$.

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Source and history

task_id
f61039c7-87f6-5329-a26a-bb199cbf545d
task_key
test--f61039c7-87f6-5329-a26a-bb199cbf545d
task_revision_id
1
config / split
/ test

Official source

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