A binary puzzle with extra signs
Sun and Moon is a binary puzzle. Every cell holds one of two symbols, and the rules keep the two in balance. Grids like this are known by several names, including Binairo and Takuzu. This version uses a 6×6 grid with three rules. Each row and column holds three suns and three moons. No three of the same symbol sit next to each other. Every = and × sign between two cells must be obeyed.
Because there are only two symbols, every deduction works the same way. Once a cell can't be a sun, it is a moon. You never weigh three or four options. You are always asking one yes-or-no question.
Four patterns to spot on sight
Most of a solve comes from a few patterns. Learn to see them without counting.
- The pair. Two suns side by side must have a moon on each end. A third sun there would make three in a row. The same goes for two moons.
- The gap. A sun, an empty cell and another sun means the middle is a moon. Filling it with a sun would join three suns.
- The full count. When a row or column already has three suns, every empty cell left in it is a moon.
- The = pair. An = sign joins two cells that hold the same symbol. You don't know which yet, but it already works like a pair. The cells just outside it on the same line must both be the opposite symbol, so they match each other.
The × sign is useful for counting. A × pair always holds one sun and one moon, so it adds one of each to its line. Here is an example. Say a row has two suns already placed, and two of its empty cells are joined by a ×. That × pair brings the third sun, so the row's suns are used up. Every other empty cell in that row is a moon. You found them without knowing which side of the × the sun is on.
How to move through a grid
Start with the locked clues and the signs, since that is where the pairs and gaps are. Fill every cell you can, then go row by row and column by column checking counts. A new symbol in a row often finishes a pattern in a column, so switch direction after each find.
The edges of the grid are worth a second look. A line of six has little room. If the first two cells of a row are suns, the third must be a moon. Then only one sun is left for the last three cells. That limits where the moons can sit without making three in a row.
When the easy patterns run out, try a short what-if. Pick a cell with two strong neighbours and imagine it as a sun. If that quickly forces three in a row or a fourth sun somewhere, the cell must be a moon. Keep these chains to two or three steps. Every grid has a single answer you can reach by logic, so a long chain usually means you missed a simpler pattern.
Common slips
- Checking only rows. The column rules are just as strict, and columns are easier to forget because you read across.
- Treating the conflict colour as a guide. The board marks three in a row and too many of one symbol. It does not mark a symbol that is wrong but still legal. A clean-looking board can still be on the wrong track.
- Losing track of × pairs when counting. Count each × pair as one sun and one moon before you decide a line is full.
- Clearing too fast. Clear wipes the board back to the clues. If one cell is wrong, tap it through the cycle instead.
Getting faster
There is one board size, so you improve through speed and fewer hints rather than bigger grids. Hint reveals one correct cell and locks it in as a clue. The end screen shows your time, moves and hints, so you can track progress. Try a few boards with no hints at all, then try to beat your time. If you like the counting side of this puzzle, Queen Zones uses the same row-and-column thinking with different pieces.
