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NZ-NZMO 2024 Problem 7

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Some of the 80960 lattice points in a 40×202440 \times 2024 lattice are coloured red. It is known that no four red lattice points are vertices of a rectangle with sides parallel to the axes of the lattice. What is the maximum possible number of red points in the lattice?

Dataset text NuminaMath olympiads. Quoted with source.

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