Medium 6x6
Tap a cell to cycle it through sun, moon and empty. The shaded cells are fixed. With a keyboard, focus the board, move with the arrow keys, and press S or 1 for a sun, M or 0 for a moon, Backspace to clear. Broken rules show up in red straight away.
Hint marks the cells it's talking about and tells you why, and Apply fills them in. Tick Show 0 and 1 if you'd rather play with digits: a sun is 1 and a moon is 0.
The rules
- Fill every cell with a sun or a moon.
- Each row and each column has the same number of suns and moons: 3 of each on a 6x6 board, 5 of each on 10x10.
- No more than two of the same side by side, across or down. Three suns in a row is never allowed.
- An = between two cells means they're the same. A × means they're different.
Every board has exactly one solution, and you can always find the next cell by reasoning. You never have to guess and check.
Binary puzzle, takuzu, binairo: what's the difference?
They're the same family. The classic binary puzzle, also known as takuzu or binairo, uses 0 and 1 and has one more rule: no two rows may be identical, and no two columns either. It has no signs.
The sun and moon version drops the identical rows rule and uses the = and × signs instead, which makes small boards a lot more interesting. The boards on this page follow the sun and moon rules. The half and half rule and the no three in a row rule work the same in both, and so do all the steps below.
Where the boards come from
The boards are made in your browser by the generator from my Sun and Moon app, with the same four levels. It fills a random grid that follows the rules, adds a few signs that agree with it, and then takes symbols away one at a time. After each one, a solver that only uses the six steps below tries to finish the board. If it can't, the symbol goes back. So every board can be solved step by step, and a separate search checks there's only one answer.
The levels differ in which steps they need. Easy boards keep at least 10 symbols and never need the last step, Balance. Medium boards need it at least once, Hard 8x8 boards at least twice, and Expert 10x10 boards five times or more. Hint uses the same solver, so it always shows the simplest step that works from where you are.
The six steps, simplest first
I'll call rows 1, 2, 3 from the top and columns 1, 2, 3 from the left. In the pictures, the cells the step looks at have an orange outline, and the cell it fills is shaded with the answer shown faintly. Every picture is a real position from a real board, and the site checks each step again before it goes up.
1. Pair: two in a row block both ends
Two suns side by side mean the cells on either end must be moons. Same for two moons. This is the step you'll use most.
2. Gap: a cell between two of the same
A sun, an empty cell, then another sun. Whatever goes in the middle would touch both, so it has to be a moon.
3. Sign: follow the = and ×
Once one side of a sign is filled, the other side follows. Next to a sun, = means sun and × means moon. Look for signs touching a filled cell every time you place something.
4. Count: half full means the rest is the other symbol
When a line already has its share of one symbol, every empty cell left in it is the other one. On 6x6 boards that's three suns or three moons. Count every line you've just added to.
5. Sign pair: an = next to a symbol
Two empty cells joined by = must match each other. If they sit next to a sun, they can't both be suns, because that would make three. So both are moons.
It looks like nothing is known about those cells until you see it.
6. Balance: every way to finish the line agrees
This is the step the harder boards are built around. When a line is partly filled and none of the simple steps apply, list the ways to finish it.
Count how many suns and moons it still needs, then try placing them without making three in a row or breaking a sign. Often only a few ways work, and they all agree on one cell.
You don't need to write the options out every time. With practice you'll spot the common shape: a line that needs two of one symbol and has to keep them apart usually forces something between or around them.
A routine for any board
- Start with the signs.
Any sign touching a fixed cell gives you a cell for free.
- Sweep for pairs and gaps.
Go row by row, then column by column. Each new symbol can create a new pair or gap, so sweep again after you place a few.
- Count every line you touch.
The moment a line has half of one symbol, fill the rest.
- Look for = next to a filled cell.
Sign pairs are easy to miss because both cells are empty.
- Only then balance.
Pick the line with the fewest empty cells and list how it can be finished. Short lists come from nearly full lines.
Mistakes that cost the most time
Guessing on a big board. A guess can run for ten moves before it breaks a rule, and by then it's hard to tell which symbol was wrong. If you're stuck, ask for a Hint instead. It'll point at a step you missed.
Forgetting the columns. It's natural to read rows. But half of all the steps on a board are in columns, and Count in a column is easy to miss.
Reading = as "both suns". An = only says the two cells match. They could both be moons.
Questions
Is this the same puzzle as Tango on LinkedIn?
It's the same idea: suns and moons, half of each per line, no three in a row, and = and × signs. These boards are my own, made by my generator, and this site has nothing to do with LinkedIn.
Does every board have only one solution?
Yes. The generator only keeps a board when the step by step solver can finish it, and a full search confirms there's no second answer.
Do I ever need to guess?
No. Every board on this page can be solved with the six steps above. Hint shows the next one whenever you're stuck.
Why are there no identical rows rules here?
That rule belongs to the classic 0 and 1 version. The sun and moon version uses signs instead. Two rows of a finished board can match, and that's fine.
Is there a version for my phone?
Yes. My Sun and Moon app for Android has 800 boards in four packs from 6x6 to 10x10, a daily board, hints that explain each step, and color blind patterns. It works offline.
Next time you're stuck, don't guess. Find the line with the fewest empty cells and count it. There's almost always a step hiding there.
Sun and Moon
800 boards from 6x6 to 10x10, a daily board, hints that explain each step, and color blind patterns.