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max of |a_1 - 1| + |a_2-2|+...+ |a_n- n| where a_i is permutation of i

Source: 1957 Hungary - Kürschák Competition p3

October 10, 2022
algebrainequalitiespermutationcombinatorics

Problem Statement

What is the largest possible value of ∣a1−1∣+∣a2−2∣+...+∣an−n∣|a_1 - 1| + |a_2-2|+...+ |a_n- n| where a1,a2,...,ana_1, a_2,..., a_n is a permutation of 1,2,...,n1,2,..., n?
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