Does it have to do with the number of stones in a given area?
We know that a single stone along the main diagonal is green. Could you give us a board with a black stone on every intersection where having just a single stone on that intersection would make the board green? Basically Iām just asking about a single black stone at 1-2, a single black stone at 1-3 etc, but itās maybe more convenient to package all that information into one picture.
Not quite. The number of stones donāt matter, but youāre on the right track.
A single stone anywhere on the board will produce a green result.
2 Likes
1 Like
Could you give an example of a green board with a maximum number of stones? (i. e. is there a green board with 48 stones, or else 47, 46 etc?) So far all of the very full boards have been red.
Iām taking more and more liberties with the rules of the game, but I think asking questions like this might be more fun than getting an outright hint 
2 Likes
I was just about to ask, if a board filled with stones of one color except for one empty intersection, is always red.
1 Like
That missing white stone is only to make the board position legal. If it was legal to have a white stone there without capturing black, it would still be green.
Yes, always.
3 Likes
I think this is a good approach for generating hints. Instead of guessing an āif and only ifā type of rule for being green, we could guess rules of the form āif ā¦ then greenā or āif ā¦ then redā. These could help refine outer and inner bounds on the green zone, as opposed to defining it outright.
1 Like
If liberties doesnāt matter for your rule, I think it makes sense to drop the requirement that the koan must be a legal go position. It just confuses things a bit, like it did with the last rule.
1 Like
Iām thinking maybe the rule refers to the āFirst Lineā, āSecond Lineā, āThird Lineā or āFourth Lineā (a.k.a. Tengen) in some way.
2 Likes
Can I ask about this Koan?
1 Like
2 Likes
For a while I was trying all kinds of variations counting how many stones were on a particular line in that sense, or difference between ones of the two colours, and patterns in odd/even numbers or if there was something about them increasing or decreasing etc.
The only other notion of area that might make sense to me is to count the boxes in the background that the stones are partially covering. That is the stones partly cover empty squares and sit on the corners of them.
If the number of stones doesnāt matter, maybe the rule is some logical expression building upon the Truth / False -values of statements such as
p = (There exists a black stone on the first line),
pā = (There exists a white stone on the first line)
(So an example would be {(p and not pā) or (not p and pā)})
1 Like
1 Like
Here are a couple of freebies:
1 Like
But actually though, if I look at those two and think, oh the left one has rectangles and squares with even sidelengths and the right picture has oddxeven side lengths. Or the left has 1x1, 3x1 and 3x3 boxes while the right has 1x2 2x3 boxes, I have no way to generalise that to when things arenāt enclosed at all.
5 Likes