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Omni-MATH / Let S={1,2,…2016}, and let f be a randomly chosen bijection from S to itself. Let n be the smallest positive integer such that f^((n))(1)=1, where f^((i))(x)=f(f^((i−1))(x)). What …

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problem

Let S={1,2,…2016}S=\{1,2, \ldots 2016\}, and let ff be a randomly chosen bijection from SS to itself. Let nn be the smallest positive integer such that f(n)(1)=1f^{(n)}(1)=1, where f(i)(x)=f(f(i−1)(x))f^{(i)}(x)=f\left(f^{(i-1)}(x)\right). What is the expected value of nn?
Plain-text mathematical notation (without MathML)
Let S={1,2,…2016}, and let f be a randomly chosen bijection from S to itself. Let n be the smallest positive integer such that f^((n))(1)=1, where f^((i))(x)=f(f^((i−1))(x)). What is the expected value of n?
Original LaTeX notation
Let $S=\{1,2, \ldots 2016\}$, and let $f$ be a randomly chosen bijection from $S$ to itself. Let $n$ be the smallest positive integer such that $f^{(n)}(1)=1$, where $f^{(i)}(x)=f\left(f^{(i-1)}(x)\right)$. What is the expected value of $n$?

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Source and history

task_id
cc851172-6756-5f01-8113-07042a1faddc
task_key
test--cc851172-6756-5f01-8113-07042a1faddc
task_revision_id
1
config / split
/ test

Official source

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