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!