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No right triangle on a grid

Source: Kyiv City MO 2023 7.4

May 14, 2023
combinatorics

Problem Statement

For n≥2n \ge 2 consider n×nn \times n board and mark all n2n^2 centres of all unit squares. What is the maximal possible number of marked points that we can take such that there don't exist three taken points which form right triangle? Proposed by Mykhailo Shtandenko
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