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Omni-MATH / Let S₇ denote all the permutations of 1,2,…,7. For any …,letf(…bethesmallestpositiveintegerisuchthatπ(1),π(2),…,π(i) is a permutation of 1,2,…,i. Compute …

Problem

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problem

Let S7S_{7} denote all the permutations of 1,2,…,71,2, \ldots, 7. For any \pi \in S_{7},let, let f(\pi)bethesmallestpositiveinteger be the smallest positive integer isuchthatπ(1),π(2),…,π(i) such that \pi(1), \pi(2), \ldots, \pi(i) is a permutation of 1,2,…,i1,2, \ldots, i. Compute \sum_{\pi \in S_{7}} f(\pi)$.
Plain-text mathematical notation (without MathML)
Let S₇ denote all the permutations of 1,2,…,7. For any \pi \in S_{7},letf(\pi)bethesmallestpositiveintegerisuchthatπ(1),π(2),…,π(i) is a permutation of 1,2,…,i. Compute \sum_{\pi \in S_{7}} f(\pi)$.
Original LaTeX notation
Let $S_{7}$ denote all the permutations of $1,2, \ldots, 7$. For any \pi \in S_{7}$, let $f(\pi)$ be the smallest positive integer $i$ such that \pi(1), \pi(2), \ldots, \pi(i)$ is a permutation of $1,2, \ldots, i$. Compute \sum_{\pi \in S_{7}} f(\pi)$.

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Source and history

task_id
b42335aa-62d7-591f-a477-7c2f7bcb60bb
task_key
test--b42335aa-62d7-591f-a477-7c2f7bcb60bb
task_revision_id
1
config / split
/ test

Official source

initial import