the answer
No, this would not change whether the rule is satisfied or not. In other words, the rule does not care (in a direct way) about black and white chains touching each other.
Edit: I’m heading to sleep everyone. Good night!
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Good night! Hope to have it figured out when you wake up ^^
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How about:
Every black chain needs to have the same number of liberties as the total number of white stones.
Can anyone find a counterexample to this?
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It hurts so much to see that written down, it must be right!
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Having looked through all the boards so far, I’m like 95% sure there’s no counterexample there. So I think it’s correct! Apparently all I needed was for Martin to go to bed 
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I have a feeling some of the GCHQ puzzles might be easier https://www.gchq.gov.uk/information/stay-at-home-and-stay-busy-with-our-brainteasers
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Ok, I’m 99.9% sure now. I looked through all the boards again, and it also fits with this thing Martin said:
(notice that if we allowed the whole board to be filled with black stones, it would be green)
I have something special prepared for the next game so I’m gonna call dibs on hosting it, but maybe I should wait until tomorrow before starting it up? It feels like there’s not many people active right now, and it would be nice to get Martins confirmation that the rule was indeed correct before starting the next game.
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I agree. That’s got to be it!
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Well done finding it out!Game 8
For this game, valid koans are any positions on the 5x5-board (they do not have to be legal go positions).
The rule is invariant to rotating/mirroring the board, and also to switching black and white.
Now here’s the new part: You can check as many boards as you like on https://zendo.4tc.xyz/. I will not be answering questions about specific boards, or collect them in this post. I will still be here to give counterexamples to any claims about the rule, and also provide hints if necessary. I’ll make an empty wiki post below this one, where you can collect what you’ve learned so far if you want, but it’s up to you how you want to organize things.
I encourage you not to post every single board you’ve checked. Instead, check some boards of some specific form and try to learn something from that, then share your findings. For example, let’s say you test every board with just one stone and find that they are all green. Instead of posting images of all those boards, simply share the information that “Every board with one stone is green”.
If you think you found part of the rule (maybe you think that every board with two stones is also green, and haven’t found a counterexample yet, but you also haven’t checked every possibility), you can write
Conjecture: Every board with two stones is green.
and I will then either confirm the conjecture or provide a counterexample.
Good luck!
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Confirmed properties
- The rule is invariant to rotating or mirroring the board.
- The rule is invariant to switching black and white.
- If the position stays the same after rotating it 90 degrees, the board is green.
- If no two stones lie on the same gridline, the board is green.
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Let’s post the koans we checked in this post .(must be important)I checked like twenty and found this.
Like I said, please don’t post every koan you check, that will be way too many and will just make the whole thread harder to overlook. Just choose ones that you find interesting, and share those. A couple of boards at a time. And add some explanation with your thinking, don’t just post pictures of boards.
I do like the two boards you chose so far, those are good examples of green boards!
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Conjecture: Assuming there are at most two stones on the board, the rule is invariant to toroidal translation.
This is true, but I feel like I should warn that it feels a bit like it’s true “by accident”. The rule makes no mention of a torus, and in general it’s not invariant to toroidal translation (as you might’ve seen before restricting the conjecture to at most 2 stones).
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That was not every koan I checked.
Yes, I saw that after I wrote the first half of the message. Like I said, those are good choices! Just wanted to remind not to post too many 
I get that we don’t want to post everything, but heres a fun sequence where if you add one more black stone it always changes from Red to Green and vice versa. It’s a zig zag pattern with one black group.
…
I was playing around with other group sizes and liberties, and not sure I understand the pattern yet.
It’s not purely about the group size since
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I’ve played around a little bit, and this seems interesting to me:
Adding white stones in the middle of this diagram does not change the color (at least the white configurations I tried did not). Adding white stones to the corners turned the color to red unless the added white corner stones are symmetrical.