I think those two are still interesting.
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A good question to ask would be, if you reverse colours, do the koans change?
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If you reverse the colors, some Koans change, yet some don’t.
I think these examples are missing from the main post.
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Thank you! I added them now.
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I’d like to revert the colors of 22, or does anyone have a more sophisticated suggestion?
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So is it an official guess, or do you want to continue the discussion first?
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Let’s make it official. 
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It seems the rule is still possibly translation and rotation invariant as far as we have discovered through our koans, but it is not symmetric with respect to colour, nor is it anti-symmetric (in the sense that the switching the colours switches between a red koan to green and in reverse).
I’m wondering what happens if we take unions:
Red + red
Green + green
Red + green
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Green+Green = Green
Red+Green = Red
So it’s more likely to be a rule along the lines of “all things must have some property” than “there must be at least one thing with some property”.
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One observation of what distinguishes green from red koans: Either no black stones are touching white, all black stones are touching white or black has only one chain.
And what about:
?
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Oops, somehow I missed that one, sorry.
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Might as well make that a guess and ask for a counterexample from @martin3141
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Good observation, but here are counter examples:
Unfortunately I can’t edit to the first post anymore.
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Kind mods, please wiki it for us.
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First post is wiki now
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I think everyone else meant that first post
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