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Grid with rooks

Source: ARO Regional stage 2022 9.3

February 16, 2023
combinatoricsRussia

Problem Statement

Given is a positive integer nn. There are 2n2n mutually non-attacking rooks placed on a grid 2n×2n2n \times 2n. The grid is splitted into two connected parts, symmetric with respect to the center of the grid. What is the largest number of rooks that could lie in the same part?
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