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We have our every day plane $\mathbb{R}^2$ which we want to paint using two colors in such a way that no four points form a square of the same color. This means that for any square on the plane its vertices have different colors.

Is it possible to paint a plane in such a way?

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  • $\begingroup$ And what have you tried so far? $\endgroup$
    – Ѕᴀᴀᴅ
    Commented May 15, 2018 at 9:12
  • $\begingroup$ @AlexFrancisco I have been thinking about using tools like in the two point set problem. Do you think it is a good approach? $\endgroup$
    – Fallen Apart
    Commented May 15, 2018 at 9:14

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