MathDB

A3

Part of 2021 IMO Shortlist

Problems(1)

Minimize Expression Over Permutation

Source: 2021 ISL A3

7/12/2022
For each integer n≥1,n\ge 1, compute the smallest possible value of ∑k=1n⌊akk⌋\sum_{k=1}^{n}\left\lfloor\frac{a_k}{k}\right\rfloor over all permutations (a1,…,an)(a_1,\dots,a_n) of {1,…,n}.\{1,\dots,n\}.
Proposed by Shahjalal Shohag, Bangladesh
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