Step 3 of 5
Balance
Three of one symbol in a line, and the rest of the line is decided.
The rule of thumb: A row or column already has its three of one symbol: every other cell takes the other symbol.
Every row and column holds exactly three suns and three moons. Once a line has its three suns, every empty cell left in it is a moon, however many there are and wherever they sit.
Pairs and Sandwich only see neighbors. Balance sees the whole line, so it can fill cells that are far from anything. These boards need it: the neighbor rules alone run dry before the end.
Where to look: Lines that are half filled or more. Count each symbol; three of either means the line is ready to finish.
Worked example
A real position from a board that needs Balance. Purple: what the reasoning rests on. Dashed: the cell in question. Green: what it proves (“this cell” in the text).
That’s all three line rules. Next: the signs between the cells. Step 4: Link →