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MathNet 2016-part-07 — 182 problems (EN–VI) Question 68

Math Olympiad Vault · MathNet 2016-part-07 — 182 problems (EN–VI)

Question 68

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 $n$?