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HMMT November 2015 H5

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Consider a 5×55 \times 5 grid of squares. Vladimir colors some of these squares red, such that the centers of any four red squares do not form an axis-parallel rectangle (i.e. a rectangle whose sides are parallel to those of the squares). What is the maximum number of squares he could have colored red?

Dataset text NuminaMath olympiads. Quoted with source.

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