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Can you paint a 6x6 grid in red, green and blue, such that its every 3x3 sub-grid contains exactly 5 red, 3 green and 1 blue cell?

Good luck!

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Will this work?

$r r r r r r$
$r b r r b r$
$g g g g g g$
$r r r r r r$
$r b r r b r$
$g g g g g g$

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  • $\begingroup$ You've go it! In fact there is a simple algorithm that can find solutions for arbitrary grid sizes, number of colors and their counts. $\endgroup$ – Dmitry Kamenetsky Oct 1 '19 at 0:47
  • $\begingroup$ @DmitryKamenetsky, nice! Thanks. $\endgroup$ – ppgdev Oct 1 '19 at 0:52
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The simple answer:

Yes. (I can paint it in such a way)

Reasoning

There are at least $9!/3!5!=504$ different arrangements that work
My method of producing them is to take any 3 x 3 grid that satisfies the condition, and tile it into a 6 x 6 grid.
This works because any 3 x 3 sub-grid of a 6 x 6 always contains the same cells of the original 3 x 3 grid.

6 x 6 Grid

There are possible arrangements that are not tilings like these, but I have not looked for them.

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