Like I had written and posted the message, but then I saw that you had edited the original message I was responding to, so I edited mine to add a response… anyways it’s messy, let’s just forget about it 
So it is simatrical?
How about another game? 
I tried really hard to make this one simple, but I guess we’ll see.
For this game we are using a 7x7 board. I’d prefer if koans are created through this version of the koan tool, just to make marking red/green less tedious.
Green Koans
Red Koans
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Do you want to give some properties for free (rotational symmetry etc), or let us work it all out ourselves?
In any case, I’ll start with this one:
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We do have rotational symmetry, but for now I can’t really think of any other freebies to give. I’m happy to respond to direct questions and guesses though.
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Guess: no white stones are directly adjacent to any black stones
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Here’s a counterexample:
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Rule guess: Every chain has an even number of liberties.
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Counter examples:
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As usual I’m interested in the color of the empty board:
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Empty board is red.
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Rule guess: There are at least two black chains, and every white chain has exactly 6 liberties.
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Counter attack:
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I’d like to try this Koan, which is a small variation from a revealed Koan:
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I’ll continue modyfing the same board:
I’ll also ask about these two, modifying one of our few green boards:
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Koans nr. 60 and 61 have different colors, yet the number of black / white stones is the same, and neither has adjacent stones.
This makes me think the rule has an element that is not about connectivity / chains / whether or not chains are adjacent to each other.
How about this Koan?
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