How to play

A binary puzzle is a square grid with an even number of rows and columns. Some cells start with a 0 or a 1. You fill in the rest.

1. Each cell holds a 0 or a 1.
2. Every row and every column has the same number of 0s and 1s. In a 10×10 grid that is five of each.
3. No row or column may contain three of the same digit next to each other. 0 0 1 is fine, 0 0 0 is not.
4. No two rows may be identical, and no two columns may be identical.

That is all. The puzzle uses no arithmetic, only these three rules, and each one has exactly one solution.

Strategy

The techniques build on each other. The first two solve most of an easy grid.

• Pairs. Two equal digits next to each other must be fenced in by the opposite digit on both sides. After 1 1, the next cell is 0, and so is the cell before.
• Sandwiches. A gap between two equal digits takes the opposite digit. In 0 _ 0 the middle cell must be 1, or there would be three 0s in a row.
• Counting. Once a line has its full quota of one digit, every empty cell in it gets the other digit. In a 6×6 grid, a row with three 1s fills its gaps with 0s.
• Avoid triples. Imagine placing the digits a line still needs. If an arrangement would create three in a row, rule it out. For example, if four empty cells side by side still need one 0 and three 1s, the 0 must go in one of the two middle cells.
• Unique lines. When a line has only two empty cells left, and filling them one way would copy a completed line, they must go the other way. This rule is the key to the harder grids.
• Work both directions. Every digit you place belongs to a row and a column. After each move, check both lines for a new pair, sandwich or full quota.

On large grids, look for the lines with the fewest empty cells first. They usually give the next move.

History

The binary puzzle is a young puzzle. It is usually credited to the Belgian puzzle makers Frank Coussement and Peter De Schepper, who created it around 2009. It is sold under several names: Binairo in the Netherlands and Belgium, Takuzu in France, and simply binary puzzle in English. The rules are the same under each name.

Playing on Summoned Games

• Five sizes. 6×6 Easy, 8×8 Medium, 10×10 and 12×12 Hard, and 14×14 Expert.
• Unlimited puzzles. Every game is generated fresh, with exactly one solution.
• Logic, not luck. The 6×6 and 8×8 grids can be finished with pairs, sandwiches and counting. The 10×10 and 12×12 grids also need the unique-lines rule. The 14×14 Expert grid has as few starting digits as a single solution allows, so it takes deeper reasoning.
• Daily 10×10 puzzle. One per day, the same for every player, with a streak counter.
• Live rule checking. Three in a row, too many of one digit in a line, or two matching lines light up red as soon as they happen.
• Check button. Press Check to see which of your filled cells disagree with the solution. Only these count as mistakes, so you can work freely until you choose to check.
• Line counter. Selecting a cell shows how many 0s and 1s its row and column still need.
• Undo, Erase and Hint. A hint fills one correct cell.
• Leaderboards for puzzles solved and for the fastest 10×10 solve without hints.
• Auto-save keeps your grid and timer if you leave mid-puzzle.

On a phone, tap a cell to select it and tap it again to cycle between empty, 0 and 1, or use the 0 and 1 buttons. On a keyboard, move with the arrow keys, type 0 or 1, press Space or Enter to cycle, Backspace or Delete to erase, C to check, H for a hint, U or Ctrl+Z to undo and Esc for the menu.

FAQ

Is a binary puzzle the same as Takuzu and Binairo? Yes. Binary puzzle, Takuzu and Binairo are different names for the same puzzle with the same three rules.

Can two rows be the same? No. Every row must be different from every other row, and every column from every other column.

Why is a cell red when I have not pressed Check? Red without Check means a rule is broken right now, such as three 1s in a row or two identical lines. It does not count as a mistake. Mistakes are only counted when you press Check.

Do I need to guess? Not on the 6×6 to 12×12 grids, which are all solvable by the techniques above. The 14×14 Expert grid is built to be as sparse as possible and may need longer chains of reasoning.

Is it free? Yes. The binary puzzle is free in your browser on phone or desktop, with no ads.