Attrition method approach move map
I want simply to propose looking at diagrams like (for example, in relation with the farmer's hat)
. 0 . 1 3 2
where the numbers label the number of plays made internally to capture at particular points.
So this says this much:
One method for White to capture these stones by the attrition method involves
Pass 1 Play at c, d, b
Pass 2 Play at c, d
Pass 3 Play at c.
That much reconstructs from the map. Attrition means that each pass puts Black in atari assuming all outside liberties filled. Black then captures.
We know that for success with the method the first of the plays in Pass 1 and Pass 2 must be nakade: namely c in the diagam. This isn't true for Pass 3: at this point the snapback stage is reached, and White could equally play at d. That gives another valid map:
. 0 . 1 2 3 .
We also have no reason to make Pass 1 involve b and d rather than (say) a or b. That gives
. 2 . 1 3 0.
Altogether there are a dozen maps in all that are valid.
I thought of this first in relation to the question of where the approach moves are. The answer seems to be: 2.5 at c and 1.1666... at each of a, b, c.
For a total of 6. The proverb here (Four is Five and Five is Eight and Six is Twelve) counts 5 approach moves, because the assumption is that we begin with a white stone at c (or else Black at c lives, naturally).