Every empty NoGo board a build can solve
The empty boards, with the value the recursion returns and the outcome that follows from it. The one-row boards run 0, star, switch and repeat, which is a pattern with no reason behind it that survives past six squares.
4 essays call
nogo-board. The drawing above is what it returns with no arguments at all; every
call below passes it something, because a placement that passes nothing draws whichever
member of the family the generator happens to default to rather than the one its essay argues
about.
The positions it draws
23 distinct positions, harvested by running this generator again at the options each essay passed it.
Where it is called
Changing this generator changes every one of these figures.
Particular games
Every group must keep breathing
NoGo is Go with no captures at all: a stone may be placed only if, afterwards, every group on the board still has a liberty. That makes a move's legality a fact about the whole board rather than about the squares it occupies — and a board therefore almost never breaks into independent parts. Of 117 boards here whose empty points fall into two regions, 24 are the sum of their regions and 93 are not.
Particular games
When the regions add
The rung below described the NoGo boards whose regions add as the ones with symmetric walls, and said the description was a guess made from six examples. It is wrong: fourteen symmetric boards do not add and sixteen that add are not symmetric. What replaces it is a criterion about liberties — sound on all 117 boards, provable in a line, and complete on only nine of the twenty-four.
Particular games
How thick a wall has to be
A single stone between two empty stretches of a NoGo board couples them, and the obvious repair is a thicker wall. Over 590 walled strips a thicker wall does help — and splitting the same 590 by the colour of the stones shows that thickness was never the variable. A wall of four one colour couples the sides exactly as one stone does.
Particular games
A wall that bends
On a NoGo strip, two empty stretches add when no group breathes into both — a wall of two stones of different colours does it, and the criterion explains nine of ninety-three boards and all nine that it covers. On a three-row board it explains none of 227, and not because it is less accurate. A wall across a board has to bend, a stone at the bend sees empty squares on both sides by itself, and every one of the 227 has a group breathing into both regions. The condition is unsatisfiable.
The whole library · The position index · The figures that play back