How to play Binairo

Binairo is a logic puzzle played with just two symbols. You fill a square grid so that no three identical symbols stand next to each other in a row or column, every row and every column holds the same number of each, and no two rows (or two columns) end up exactly alike. It is also known as Takuzu, binary puzzle or binary Sudoku, and on paper it is usually written with 0s and 1s. Here the two symbols are a sun and a moon.

Every puzzle here is generated fresh by the game when you start it, has exactly one solution, and can be solved by reasoning alone. You never need to guess. The four levels grow from a 6x6 grid on Easy to a 12x12 grid on Crazy, and each level asks for deeper reasoning than the one before.

How to play on skill.games

When you open the game, the settings popup appears. Choose a level under DIFFICULTY, choose how mistakes are treated under MISTAKES, and press PLAY. A new puzzle is generated in a moment.

• The board takes up most of the screen. The symbols that are already placed when the puzzle starts sit on darker grey tiles; they are part of the puzzle and can't be changed.
• Placing a symbol: tap an empty cell to put a sun in it. Tap it again to turn the sun into a moon, and once more to empty the cell. So one tap gives a sun, two quick taps give a moon.
• UNDO (under the board, or beside it when your screen is wider than it is tall) takes back your last change, all the way back to the start. Undo is free and unlimited.
• Rule breaks are drawn in red: a red ring around three alike in a row, and a red line through a row or column that holds too many of one symbol or that repeats another full line (dashed for a repeat).

The game waits a moment before it checks a cell, so passing through a sun on your way to a moon never counts against you. A cell is checked as soon as you tap a different cell, or about a second after your last tap on it.

On a computer you can also use the keyboard: the arrow keys (or W, A, S, D) move a highlighted cursor, Space or Enter cycle the cell under it, 0 puts a sun and 1 a moon, Backspace or Delete empty it, and Z undoes.

The top line shows the clock, the level, the grid size and your mistakes. The clock runs only while you play: it stops when the menu or a popup is open. The menu button in the top-left corner pauses the game, starts a new puzzle or switches the sound on or off. The game is saved after every move, so if you close the page you can press CONTINUE later and carry on with the same grid, clock and undo history.

When the last cell is filled correctly, the board lights up and the results screen shows your time, your best time at that level (a star marks a new record), your mistakes, the grid size and the puzzle's code, together with your wins, losses, win rate and streaks.

Rules

The grid. The grid is square with an even size: 6x6, 8x8, 10x10 or 12x12 here. Every cell gets a sun or a moon.

No three alike. Three suns, or three moons, may never stand side by side in a row or one above the other in a column. Two in a row are fine.

Half and half. Every row and every column holds exactly as many suns as moons: three of each on a 6x6 grid, six of each on a 12x12 grid.

No twins. No two full rows may be identical, and no two full columns may be identical.

Givens. Every puzzle starts with some symbols already placed. Every puzzle has exactly one way to complete it.

Mistakes - Unlimited (the default). When a cell you change breaks a rule - three alike, too many of one symbol in a line, or two identical lines - the break is drawn in red and the mistakes counter goes up by one. Nothing else is checked, so nothing about the solution is revealed. Because the solution is unique, a full grid with no red marks is always the right one.

Mistakes - 3 lives. Every cell you fill is checked against the solution once it settles. A wrong symbol costs a life: the cell turns to the right symbol, is marked with a small red dot and can't be changed again. The third mistake ends the game and counts as a loss.

Abandoned puzzles. Starting a new puzzle before finishing the current one counts as a loss in your statistics for that level.

Solving techniques

These are the methods the game's own solver uses to grade every puzzle, from the simplest up.

• Pairs: two alike side by side - the cells on both ends must be the other symbol, or there would be three in a row.
• Gaps: two alike with one empty cell between them - the middle must be the other symbol.
• Full count: a row that already has all its suns gets moons everywhere else, and the other way round.
• One left: when a line needs just one more sun, try every place it could go. If putting it in a cell would force three moons together somewhere else in the line, that cell can't take the sun. Cells that come out the same every way are settled. The same check catches a line that would copy a finished line.
• Whole-line analysis: the same idea for any line, whatever is left to place - list the ways the line can still be completed, without three alike, with the right counts and without copying a finished line, and fill in what they all agree on.
• Two lines together: take two rows (or two columns) one or two apart and try their completions in pairs. A pair can be impossible even when each line alone is fine - for example when together they would put three alike in a column, or give a column too many of one symbol. What every possible pair agrees on is settled.

Strategy tips

• Hunt pairs and gaps first. They are everywhere at the start, and each one you fill creates new ones.
• Count constantly. Keep an eye on how many suns and moons each line still needs. A line that needs only one more of a symbol is close to being solved.
• Watch the edges of a gap of three. In a line that needs one sun, three empty cells side by side must hold it, so every other empty cell is a moon.
• Compare nearly finished lines with finished ones. A line with two empty cells that matches a full line everywhere else must be filled the opposite way.
• Look across two lines. On the bigger grids, two rows that are each still open can rule each other out through the columns they share.
• Don't guess. Every puzzle here can be solved by logic. If you feel stuck, count again - the answer is usually a line that needs just one more of something.

Difficulty levels

The game generates every puzzle on the spot and grades it with a solver that works the way a person does, always using the easiest step available. A puzzle is given to you only if its hardest required step matches the level you chose.

• Easy: a 6x6 grid; pairs, gaps and full counts are all you need.
• Normal: an 8x8 grid; at least one step needs the one-left check.
• Hard: a 10x10 grid; at least one step needs whole-line analysis.
• Crazy: a 12x12 grid; at least one step needs two lines worked out together.

Statistics and best times are kept separately for each level. If Binairo is new to you, start on Easy and move up once the pairs and gaps jump out at you.