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Easy inequality with integer variable

Source: China Additional TST for IMO 2020, P5

October 20, 2020
inequalitiesalgebra

Problem Statement

Let a1,a2,⋯ ,ana_1,a_2,\cdots,a_n be a permutation of 1,2,⋯ ,n1,2,\cdots,n. Among all possible permutations, find the minimum of ∑i=1nmin⁡{ai,2i−1}.\sum_{i=1}^n \min \{ a_i,2i-1 \}.
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