Let $p_1, p_2, . . . , p_{30}$ be a permutation of the numbers $1, 2, . . . , 30.$ For how many permutations does the equality $\sum^{30}_{k=1}|p_k - k| = 450 $ hold?
Source: Baltic Way 2014, Problem 7
Tags: combinatorics proposed, combinatorics
Let $p_1, p_2, . . . , p_{30}$ be a permutation of the numbers $1, 2, . . . , 30.$ For how many permutations does the equality $\sum^{30}_{k=1}|p_k - k| = 450 $ hold?