THE SETUP
Takuzu has two names because it was popularised in different countries under different brands. Binairo is the European name; Takuzu is the name used in competitive puzzle circles. The rules are identical:
- No three in a row: you cannot place three consecutive identical symbols in any row or column.
- Balance: every row and every column must contain exactly N/2 zeros and N/2 ones (so grids are always even-sized: 6×6, 8×8, 10×10).
- Uniqueness: no two rows may be identical, and no two columns may be identical.
The puzzle starts with some cells pre-filled. Your job is to complete the grid so all three constraints hold simultaneously.
WHY THREE IN A ROW DOES MOST OF THE WORK
The no-three-in-a-row rule is the most productive constraint — it fires constantly and forces placements immediately. If you see two consecutive identical symbols anywhere in a row or column, the cell on either side of them must be the opposite symbol to avoid creating a triple.
It also runs backward: if a cell has the same symbol two cells away (with a gap between them), the gap cell must be the opposite symbol — otherwise placing the matching symbol there would create a triple with one of the bookends.
Example: 1 _ 1 in any row — the blank must be 0. If it were 1, you'd have 1 1 1.
Beginners who scan only for adjacent pairs miss the skip pattern. Scan for both when reading each row and column.
BALANCE ARITHMETIC
The balance rule turns into pure arithmetic: a row of length N needs exactly N/2 zeros and N/2 ones. Count how many zeros and ones are already placed in a row. If you've hit the quota for one symbol, every remaining blank in that row must be the other symbol.
This often fires in the middle or late game, when several cells are placed and the row is close to full. It's the Takuzu equivalent of naked singles in Sudoku — obvious once you count, invisible if you don't.
Example: a 6-cell row needs 3 zeros and 3 ones. If 3 zeros are already placed, every remaining blank is a 1.
UNIQUENESS: RARE BUT DECISIVE
The no-duplicate-rows rule fires less often than the other two, but when it fires, it resolves an entire row at once. If you have two rows that are currently identical except for one blank, that blank cannot be filled with the value that would make the rows identical — you're forced to the other value.
On harder puzzles, you may reach a point where three-in-a-row and balance have both stalled. Scan the rows you haven't fully placed against each other. A near-duplicate pair almost always unlocks the next move.
THE SOLVE ORDER
- Three-in-a-row first: scan every row and column for adjacent pairs and skip patterns. These are the cheapest and most productive moves. Do a full pass before anything else.
- Balance second: count placed symbols in each row and column. If a quota is met, fill all remaining blanks.
- Uniqueness last: compare near-complete rows to each other. If two rows are one blank apart from being identical, that blank is forced.
- Repeat: each placement creates new adjacent pairs and changes row/column counts. Start the cycle again from step 1 after every batch of placements.
That order — three-in-a-row → balance → uniqueness — is the complete strategy for beginner and intermediate grids. Harder puzzles are longer and the gaps between forced moves are smaller, not fundamentally different in technique.
HOW IT COMPARES TO SUDOKU
Sudoku has 9 symbols and the no-repeat rule within units. Takuzu has 2 symbols and instead uses a balance constraint plus no-three-in-a-row. The underlying reasoning style is the same — elimination and forced placements — but Takuzu's smaller symbol set makes each constraint immediately visible without tracking nine candidates.
Takuzu is often described as an easier entry point to logic puzzles than Sudoku because you never juggle more than two options per cell. That's true in one sense. But the three-rule interaction on a large 10×10 grid can produce surprisingly long deduction chains, and the uniqueness constraint has no analogue in standard Sudoku at all.