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Minimize Expression Over Permutation

Source: 2021 ISL A3

July 12, 2022

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Problem Statement

For each integer

n\ge 1,

compute the smallest possible value of

\sum_{k=1}^{n}\left\lfloor\frac{a_k}{k}\right\rfloor

over all permutations

(a_1,\dots,a_n)

of

\{1,\dots,n\}.

Proposed by Shahjalal Shohag, Bangladesh

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