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Find the number of permutations!

Source: CIIM 2022 - Problem 4

September 19, 2023
permutationscountingnumber theoryDivisibility

Problem Statement

Given a positive integer nn, determine how many permutations σ\sigma of the set {1,2,…,2022n}\{1, 2, \ldots , 2022n\} have the following property: for each i∈{1,2,…,2021n+1}i \in \{1, 2, \ldots , 2021n + 1\}, the number σ(i)+σ(i+1)+⋯+σ(i+n−1)\sigma(i) + \sigma(i + 1) + \cdots + \sigma(i + n - 1) is a multiple of nn.
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