Go Zendo

[RubyMineshaft]

I fixed the issues with my version of the koan tool if that would be helpful. Sorry, I didn’t realize it had broken.

[Feijoa]

The one about triangles earlier was also equivalent to the stones being in a line so that’s probably not it this time.

[martin3141]

Thank you! That helps a lot I’ve updated the starting post with Koans generated by your tool.

For anybody who doesn’t have the link: https://rubymineshaft.github.io/

[mafidufa]

Zendo has been on my list of games to get, though I worry that it would end up as rarely used as my Go board.

Here’s my question.

[martin3141]

[Feijoa]

Another possibility is that the black and white stones are related by translation instead of rotation. Maybe someone can propose a position to distinguish between rotation and translation.

[Feijoa]

It could even be as simple as “no black and white stones touching.”

[Vsotvep]

[martin3141]

[Vsotvep]

I’d like to try a position where Black is not a rotation or translation of White, and a position where Black and White stones touch.

[mafidufa]

I notice that all positions submitted so far have equal numbers of black and white stones, including the single red koan we have.

[Leira]

I’ll submit a guess.

How about this one.

[martin3141]

[Vsotvep]

Alright, so no-touching is out.

Previous ideas that could still be correct:

• Black and White shape are translations and/or rotations of each other
• All stones of each colour need to be in a line (although equivalent to an earlier koan)

Some new ideas:

• Every connected group has the same number of stones
• The smalles rectangle fitting all Black stones has the same dimensions as the smallest rectangle fitting all White stones

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It’d be nice to find a position that gives us another red koan. It should be easy to find an example breaking all above rules, but perhaps someone else has more ideas of what the answer could be?

[Feijoa]

I could submit a weird rotation that’s very likely to be red if nobody has an idea for one that breaks everything.

[Vsotvep]

If translation and/or rotations of White to Black always give us a green koan, we should also check for reflections and for scaling.

Perhaps a scaled reflection?

[Jon_Ko]

I’m suggesting to guess a kosumi for one color and a keima for the other one.

Edit: Okay no, but some stones could be added to that, to break lines and such.

[martin3141]

[Vsotvep]

Still green!

Let’s see what this variation of the only red koan will bring us:

[Leira]

They form the same geometric shape. That is to say, 15 were both triangles.

If that hypothesis is true @Vsotvep 's last koan should be red (a line vs a quadrilateral)

Edit: I do see a few problems with this idea though, for example, if it were true, is it just the convex hull?