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Omni-MATH / Given a permutation π of the set {1,2,…,10}, define a rotated cycle as a set of three integers i,j,k such that i<j<k and π(j)<π(k)<π(i). What is the total number of rotated cycles …

Problem

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problem

Given a permutation π\pi of the set {1,2,…,10}\{1,2, \ldots, 10\}, define a rotated cycle as a set of three integers i,j,ki, j, k such that i<j<ki<j<k and π(j)<π(k)<π(i)\pi(j)<\pi(k)<\pi(i). What is the total number of rotated cycles over all permutations π\pi of the set {1,2,…,10}\{1,2, \ldots, 10\} ?
Plain-text mathematical notation (without MathML)
Given a permutation π of the set {1,2,…,10}, define a rotated cycle as a set of three integers i,j,k such that i<j<k and π(j)<π(k)<π(i). What is the total number of rotated cycles over all permutations π of the set {1,2,…,10} ?
Original LaTeX notation
Given a permutation $\pi$ of the set $\{1,2, \ldots, 10\}$, define a rotated cycle as a set of three integers $i, j, k$ such that $i<j<k$ and $\pi(j)<\pi(k)<\pi(i)$. What is the total number of rotated cycles over all permutations $\pi$ of the set $\{1,2, \ldots, 10\}$ ?

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Source and history

task_id
05949ea2-cff2-57b9-b686-ed8855ba7153
task_key
test--05949ea2-cff2-57b9-b686-ed8855ba7153
task_revision_id
1
config / split
/ test

Official source

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