Go Zendo

Rule guess: When a White chain touches a Black chain, they must have the same number of liberties.

Do you allow positions that have an unequal number of White stones and Black stones? I guess it would be hard to prove that they cannot occur in a go game, since there could have been captures.

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Koan_22

Good guess, but here are (additional) counter-examples:

Koan_23
Koan_25

Yes, I just require that all chains have at least one liberty.

With passes allowed, I believe all such positions can be reached in a normal go game, even without captures. With passes not allowed, that could be an interesting question. But a question for another thread :wink:

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Symmetry broken?

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Differences I can spot:

Black/White reversed
Rotated 90’
4 stone chain starting on 4,3 vs 5,2

None of which I can tie into the other koans we have seen

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I’d try to undo some of those changes to create another red koan, we still haven’t produced one on our own.

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Hypothesis: White is always in the minority when touching black chains.

More precisely: if you count the stones in a white chain and the stones in all black chains touching this white chain, then either you have counted more black stones than white stones, or the white chain is not touching any black stones at all.

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Sounds like 14 and 25 should be of the same color, but they aren’t?

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Not sure if it is the same, but allow me to rephrase it in a simpler manner:

“If you eliminate all the black and white chains that touch each other, there are more (or equal) white stones left than black stones”

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Alternatively, I think this is what @ArsenLapin1 meant:

“There are more (or equal) black stones in chains touching white, than white stones in chains touching black”

Anyway, I’ll submit another guess

image

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Koan_27

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Can I ask for a counterexample?

alright, here are counter examples:

Koan_28
Koan_30

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I suspect you use Katago to count the liberties, and so the count is wrong when there is a large circular group!

Here are two variations on the koans, just to see how changing a small detail affects the result:

Koan_33Koan_34

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Koan_35
Koan_37

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