Balance: How to Think in Suns and Moons

Balance is the daily puzzle newcomers underestimate. There are no numbers and only three rules, so it reads as the light one on the card. Then Thursday arrives and the board stops moving.

The rules, in full:

Fill the 6x6 board with suns and moons. Every row and every column ends with exactly three of each. Never three of the same symbol side by side. Some pairs of cells carry a clue between them: an equals sign means those two match, a cross means they differ.

That is everything. All the difficulty comes from how the three interact.

Start with the three-in-a-row rule

Most of your moves come from the ban on three in a row, and it works in two directions.

The first is easy to see. A sun beside a sun means the cells on either side of that pair have to be moons, because anything else makes a run of three.

The second is the one beginners walk past. A sun, an empty cell, then another sun means the empty cell must be a moon. Put a sun there and you have three together. That shape is the sandwich, and training your eye for it is most of what makes Monday and Tuesday quick. Before anything else, scan every row and column twice: once for adjacent pairs, once for gaps between matching symbols.

Then count

Three suns and three moons per line, always. So the moment a row holds three suns, every remaining cell in that row is a moon and you can fill them without thinking.

Counting is easy to forget, because it is a tally you keep rather than a shape you notice. When a row reaches five filled cells, check the count before anything else. Columns deserve the same check and rarely get it, since the eye reads horizontally by default.

Put the two together and you have the engine of the game. Counting tells you what a line still owes; the three-in-a-row rule tells you where it cannot be paid.

What the clues are actually worth

An equals or cross sign between two cells carries more than one cell's worth of information, because it survives being unsolved. Even with both cells blank, you know they move together or in opposition, so the instant one lands the other lands with it.

The habit worth building is small: when you place a symbol, check straight away whether that cell touches a clue. Beginners place a symbol, feel pleased, and move on. Quick solvers treat one placement as two whenever a clue is attached.

Crosses tend to be worth more than equals signs. A pair that must differ holds exactly one sun and one moon, which pins that pair's contribution to both its row count and its column count before you know which way round it sits.

When you hit a wall

At some point, usually from Friday on, the board stops offering forced moves. That is deliberate. We call it a wall, and it is the deep end of the game.

Do not guess at it. Pick a cell where you can see only two possibilities, assume one, and follow the consequences a few steps. Either you reach something illegal, in which case the other option was right and you have earned a real deduction, or nothing breaks, in which case you undo and try elsewhere.

Depth is what separates that from guessing. Our walls are built to break within a few steps, and we cap how deep the chain is allowed to run before it gives. If you are eight moves into an assumption with no contradiction in sight, you are on the wrong cell: back out and pick another, ideally one near a clue or a nearly full line, where consequences pile up faster.

The test is what you are looking for. If you are hunting a contradiction, you are reasoning. If you are keeping an assumption because nothing has broken yet, you are guessing, and that is how people wreck a board they were solving correctly.

What changes as the week goes on

Early in the week you will barely meet a wall. The sandwich and the counting rule carry you. As the week climbs, free moves thin out, walls appear, and by Saturday and Sunday you will need one or two of them to finish.

What stays true is that a wall always cracks. Every board is proved solvable by reasoning before it is scheduled, and how we make the puzzles explains what that proof involves. If you are stuck, there is a shorter assumption somewhere you have not tried.

Frequently asked questions

What do the equals and cross signs mean?

An equals sign between two cells means they hold the same symbol. A cross means they hold different symbols. Both hold true even before you know which symbol either cell is.

Do I have to keep three of each per line?

Yes, every row and every column ends with exactly three suns and three moons. Treat that count as a tool rather than a restriction: it often tells you what a line needs before the pattern rules do.

Is Balance the same as Tango?

They share a family. Ours runs a fuller week: a gentle Monday, and a Sunday meant to give you one genuinely deep think rather than another two-minute fill.

How do I get unstuck without guessing?

Find a cell with only two options, assume one, and follow it a few steps looking for something illegal. If nothing breaks quickly, undo and pick a different cell, ideally one near a clue or a nearly complete line.