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Medium

PuzzlesDiscrete Maths

Consider the infinite 2D plane. Every point with integer coordinates is coloured either White, Black or Brown, in any way whatsoever. For example, $(0,0)$ might be black, $(1,2)$ might be white and so on.
No matter how the points are coloured, is it always possible to find a rectangle with sides parallel to the axes (with each corner on some integer point) which has all four corners of the same colour?

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