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BALTIC-WAY 2014 Problem 7

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Let p1,p2,…,p30p_{1}, p_{2}, \ldots, p_{30} be a permutation of the numbers 1,2,…,301,2, \ldots, 30. For how many permutations does the equality ∑k=130∣pk−k∣=450\sum_{k=1}^{30}\left|p_{k}-k\right|=450 hold?

Dataset text NuminaMath olympiads. Quoted with source.

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(15 !)^{2}

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