How to solve a binary puzzle (Binairo / Takuzu)

What is Binairo?

Binairo is a logic puzzle on an even-sized grid (6×6, 8×8, 10×10, and up). You fill each cell with either a 0 or a 1 following three rules. Some cells are pre-filled as clues. The puzzle is also known as takuzu (France/Japan), binary puzzle (Netherlands), and was popularized by the mobile game 0h h1. You might also see it called tic-tac-logic (Conceptis Puzzles' proprietary name) or simply "unruly."

Because there are only two possible values per cell, the rules interact tightly and small deductions cascade quickly. Most beginners find Binairo easier to learn than Sudoku, while still offering genuine challenge on larger grids.

The three rules

1. No three consecutive: No more than two identical digits can appear next to each other in any row or column. Sequences like 0-0-0 or 1-1-1 are forbidden. Two in a row (0-0 or 1-1) is fine.
2. Equal count: Each row and each column must contain exactly N/2 zeros and N/2 ones. In a 6×6 grid, that means three 0s and three 1s per row and column. In an 8×8 grid, four of each.
3. Uniqueness: No two rows can be identical, and no two columns can be identical. Every row must be a distinct binary sequence, and every column must be a distinct binary sequence.

That is the complete rule set. No arithmetic, no special regions, no complex notation. Just three constraints on binary digits.

Worked example: 6×6 grid

Suppose you have a 6×6 grid. Row 1 has cells: _, 0, 0, _, _, 1. Each row needs three 0s and three 1s.

Step 1 — Consecutive forcing. Cells 2 and 3 both hold 0. The cell on either side (cells 1 and 4) must be 1 to avoid three consecutive 0s. Row 1 is now: 1, 0, 0, 1, _, 1.

Step 2 — Count completion. Row 1 now has three 1s (cells 1, 4, and 6). Since a 6×6 row needs exactly three 1s, the remaining empty cell (cell 5) must be 0. Row 1 is complete: 1, 0, 0, 1, 0, 1.

Step 3 — Propagate. With row 1 filled, each column gains new information. Continue applying consecutive forcing and count completion down the grid. When simple techniques stall on harder puzzles, compare rows for uniqueness violations.

This is the core loop: use consecutive patterns to force digits, check counts to fill remaining cells, and verify uniqueness when rows are nearly complete.

Solving strategies

Consecutive forcing

The most common technique. When two adjacent cells hold the same digit, their neighbors must hold the opposite. Scan every row and column for pairs of identical digits and fill in the forced neighbors. After each placement, check whether new pairs have formed.

Sandwich forcing

When two cells with the same digit have exactly one empty cell between them (like 0-?-0), the middle cell must be the opposite digit. The "sandwich" pattern is easy to miss because the identical digits are not adjacent.

Count completion

Track the number of 0s and 1s in each row and column. When one digit reaches its maximum (N/2), every remaining empty cell must hold the other digit. The count display at the edges of the board helps with this.

Uniqueness elimination

On harder puzzles, uniqueness is the breakthrough technique. If two rows are identical in all their filled positions and only differ in two empty cells, those cells must be filled to make the rows distinct. This often resolves positions that consecutive forcing and counting cannot reach.

Binairo vs other puzzles

Unlike Sudoku, which uses nine different digits with box constraints, Binairo uses only two values with consecutive and counting constraints. The solving feels different: Sudoku is about tracking which digits go where, while Binairo is about pattern recognition and parity.

Nonograms also use binary cells (filled or empty), but their clues describe run lengths, not consecutive or counting rules. Futoshiki shares the constraint-propagation solving style but uses inequality symbols on a Latin square grid. If you enjoy Binairo, these are natural next puzzles to try.

Common mistakes

Overlooking the sandwich pattern. Two identical digits with one empty cell between them (0-?-0) force the middle cell just as surely as adjacent pairs. Scan for gaps as well as adjacencies.

Forgetting to count. After consecutive forcing runs, recheck the counts. A row might have reached its limit for one digit without you noticing, leaving free placements on the table.

Ignoring uniqueness until the end. On larger grids, the uniqueness rule can resolve cells early in the solve. Check for rows or columns that are developing similarly — do not wait until they are nearly complete.

Frequently asked questions