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Takuzu Strategy: A Complete 6×6 Walkthrough
Solve Takuzu by blocking triples, balancing each row and column, then comparing lines to prevent duplicates. This complete 6×6 example uses all four deductions, including the distinct-lines rule that separates classic Takuzu from Tango.
Takuzu, also called Binairo, uses two values. Here ☀ means 0 and ☾ means 1. Every row and column needs three of each, no three identical symbols can be consecutive, and no two completed rows or two completed columns may match. A row may match a column.
The four checks to repeat
- Pairs: two consecutive suns require a moon immediately before and after them, where those cells exist. Reverse the values for moons.
- Sandwiches: sun, gap, sun forces a moon in the gap.
- Balance: once a line contains three suns, its other cells must be moons; the reverse also applies.
- Distinct lines: if a nearly finished line would copy a completed line, use the other balanced ending. Compare rows with rows and columns with columns.
Do not compare unfinished lines as if their unknown cells were already equal. The walkthrough below uses a completed reference line and exactly two gaps, with one of each symbol left to place.
Solve this 6×6 Takuzu from its original clues
The source puzzle is labelled medium because it needs the distinct-lines deduction. Follow all 24 steps in order. Rows run top to bottom and columns left to right, starting at 1; keep earlier placements.
Sandwich: The suns at R1C2 and R1C4 surround this gap; another sun would make a triple. Place a moon at R1C3.
Sandwich: The moons at R4C1 and R6C1 surround this gap; another moon would make a triple. Place a sun at R5C1.
Pair: The two suns at R5C1 and R5C2 would make a triple with another sun beside them. Place a moon at R5C3.
Balance: column 1 already contains three moons, so balance fills its gaps with suns. Place a sun at R2C1, R3C1.
Pair: The two suns at R2C1 and R2C2 would make a triple with another sun beside them. Place a moon at R2C3.
Pair: The two moons at R2C3 and R2C4 would make a triple with another moon beside them. Place a sun at R2C5.
Check the board after step 6
Balance: row 2 already contains three suns, so balance fills its gaps with moons. Place a moon at R2C6.
Pair: The two suns at R1C2 and R2C2 would make a triple with another sun beside them. Place a moon at R3C2.
Sandwich: The moons at R3C2 and R3C4 surround this gap; another moon would make a triple. Place a sun at R3C3.
Balance: column 2 already contains three suns, so balance fills its gaps with moons. Place a moon at R4C2, R6C2.
Pair: The two moons at R4C1 and R4C2 would make a triple with another moon beside them. Place a sun at R4C3.
Pair: The two moons at R6C1 and R6C2 would make a triple with another moon beside them. Place a sun at R6C3.
Check the board after step 12
Pair: The two moons at R2C4 and R3C4 would make a triple with another moon beside them. Place a sun at R4C4.
Pair: The two suns at R4C3 and R4C4 would make a triple with another sun beside them. Place a moon at R4C5.
Balance: row 4 already contains three moons, so balance fills its gaps with suns. Place a sun at R4C6.
Sandwich: The suns at R4C6 and R6C6 surround this gap; another sun would make a triple. Place a moon at R5C6.
Distinct lines: row 5 matches the known positions of completed row 2. Two gaps remain, needing one of each symbol. Copying that line's ending would duplicate it, so reverse the values in those gaps. Place a sun at R5C4.
Check the board after step 17
Balance: row 5 already contains three suns, so balance fills its gaps with moons. Place a moon at R5C5.
Check the board after step 18
Pair: The two suns at R4C4 and R5C4 would make a triple with another sun beside them. Place a moon at R6C4.
Balance: row 6 already contains three moons, so balance fills its gaps with suns. Place a sun at R6C5.
Pair: The two moons at R4C5 and R5C5 would make a triple with another moon beside them. Place a sun at R3C5.
Balance: row 3 already contains three suns, so balance fills its gaps with moons. Place a moon at R3C6.
Pair: The two suns at R2C5 and R3C5 would make a triple with another sun beside them. Place a moon at R1C5.
Balance: row 1 already contains three moons, so balance fills its gaps with suns. Place a sun at R1C6.
Check the board after step 24
The finished rows and columns each contain three suns and three moons, with no triples or duplicate lines. Every step follows from the stated rules; no trial placement is needed.
Common Takuzu mistakes
- Checking only rows instead of both directions.
- Confusing distinct lines with a unique solution: these are different properties.
- Applying the distinct-lines rule to Tango, whose relationship clues use a different rule set.
- Assuming a row cannot match a column. Only two rows, or two columns, must differ.
Practise more Takuzu · Compare Tango and Takuzu · Learn Tango strategy
About this example
This is an original Solvedle practice puzzle, with a unique solution checked separately from the explained deductions. It is not a daily answer. For a publisher's statement of the classic rules, see Binairo's rules.