Sun & Moon Puzzle Guide: Balanced Rows

Rule 1 patterns: never three in a row

The no-three rule gives you two instant patterns:

• Two together: sun, sun. The squares on either side must be moons. Check both ends of every pair.
• A gap: sun, empty, sun. The empty square between must be a moon, otherwise there would be three suns.

Scan every row and column for these before anything else. They are the equivalent of sudoku's singles and clear a third of an easy grid.

Rule 2 patterns: balance

Each line has the same number of suns as moons: three each in a 6 × 6 grid, four each in an 8 × 8. So:

• If a line already has all its suns, every remaining square is a moon (and vice versa).
• If a line needs one more sun and two more squares are open, and the open squares are adjacent to two suns, the arrangement may be forced by the no-three rule as well.

Count the symbols in a line whenever a square is placed in it. Lines one symbol short of their quota are where the next placements come from.

Rule 3: the clues

An = between two squares means they hold the same symbol: once one is known, so is the other. A × means they differ. The clues matter most at the start of a puzzle, before the grid has enough symbols for the patterns: an = joined to a square that already has a symbol places another; a × between two squares in a line that is nearly balanced often decides them.

Treat a chain of clues as one unit. Three squares joined by = are all the same, which for balance counting means they use up three of a line's quota at once. Two squares joined by × are one sun and one moon between them, whichever way round.

Lookahead: the one-step test

When patterns and counting run dry, pick an open square in a line that needs one more of each symbol and ask: if this is a sun, does it break a rule? Make it a sun in your head, apply the no-three rule along its row and column, and check the balance. If it forces three in a row or too many suns somewhere, it must be a moon. This is not guessing: you are proving one option impossible, and you only need to look one or two squares away. Medium and hard days need a few of these; easy days rarely do.

A common one-step case: an open square flanked by two open squares, where placing a sun would force both neighbours to be moons, and the line then has too many moons.

Rows and columns must be different

In many binary puzzles there is a fourth rule that no two rows (or columns) may be identical. Sun & Moon does not use it, so do not rely on it; the three rules and the clues are enough for every daily grid.

A routine for each pass

1. Pairs and gaps in every row and column.
2. Clues: = and × next to placed symbols.
3. Balance: any line that has its quota of one symbol.
4. One-step lookahead on squares in lines that are one short.
5. Repeat until full. The grid is checked when complete.

Common mistakes

• Checking rows only. Every pattern applies to columns too, and the one you need is usually there.
• Forgetting the gap pattern. Sun, empty, sun is as strong as sun, sun.
• Miscounting balance. Count out loud on bigger grids: "three suns, two moons, one open".
• Treating × as "the opposite of what is there". It only tells you the two joined squares differ; if neither is placed, use it in the balance count instead.
• Cycling a square by accident. Tapping cycles sun, moon, empty; a third tap clears it, which is easy to do when hurrying.

Glossary

• Balance: the rule that a line holds equal numbers of each symbol.
• Pair: two of the same symbol together; the squares beyond them take the other symbol.
• Gap: two of the same symbol with one square between; that square takes the other symbol.
• Equals clue (=): the joined squares match.
• Cross clue (×): the joined squares differ.