Takuzu rules
Takuzu is played with two kinds of circles and three rules. You will know the rules in a minute; the fun is in spotting which rule decides the next cell.
- Never three white or three black circles next to each other in a row or a column.
- Every row and every column has as many white circles as black ones.
- No two rows are the same, and no two columns are the same.
Takuzu is also known as the binary puzzle, binary sudoku or Binairo; the rules are the same. Besides the daily grids there are unlimited binary puzzles, free online, from 6x6 to 12x12.
Try it on small grids
Three small Takuzu puzzles to get the feel. Hints work here too and explain each step.
Practice 1 · 4x4 · Easy
Practice 2 · 6x6 · Easy
Practice 3 · 6x6 · Medium
Your first moves
Scan for two equal circles side by side: the cells at both ends must be the other colour, or you would get three in a row. Then look for gaps between two equal circles, the sandwich: the gap takes the other colour. When a row already has half of one colour, the rest of the row is the other colour. These three moves finish most Easy grids.
A worked example, step by step
Our solver finished this Takuzu (6x6) in 21 steps. Every step names its technique; step through it on the board, or read the whole solve below.
All 21 steps
- Pairs. B5 and C5 are both white; a third white next to them would make three in a row, so A5 and D5 are black.
- Pairs. C2 and C3 are both black; a third black next to them would make three in a row, so C1 and C4 are white.
- Pairs. C4 and D4 are both white; a third white next to them would make three in a row, so B4 and E4 are black.
- Pairs. C4 and C5 are both white; a third white next to them would make three in a row, so C6 is black.
- Pairs. E3 and E4 are both black; a third black next to them would make three in a row, so E2 and E5 are white.
- Sandwich. B2 sits between two black circles (A2 and C2), so it is white.
- Sandwich. D3 sits between two black circles (C3 and E3), so it is white.
- Pairs. D3 and D4 are both white; a third white next to them would make three in a row, so D2 is black.
- Balance. Row 2 already has its 3 black circles, so the 1 open cell left is white.
- Pairs. F2 and F3 are both white; a third white next to them would make three in a row, so F1 and F4 are black.
- Balance. Row 4 already has its 3 black circles, so the 1 open cell left is white.
- Balance. Row 5 already has its 3 white circles, so the 1 open cell left is black.
- Pairs. F4 and F5 are both black; a third black next to them would make three in a row, so F6 is white.
- Line analysis. Of the 2 valid ways to finish row 1, every one puts white in A1.
- Balance. Column A already has its 3 white circles, so the 1 open cell left is black.
- Sandwich. B3 sits between two black circles (A3 and C3), so it is white.
- Balance. Column B already has its 3 white circles, so the 1 open cell left is black.
- Pairs. B6 and C6 are both black; a third black next to them would make three in a row, so D6 is white.
- Sandwich. E6 sits between two white circles (D6 and F6), so it is black.
- Balance. Column D already has its 3 white circles, so the 1 open cell left is black.
- Sandwich. E1 sits between two black circles (D1 and F1), so it is white.
Common mistakes
- Checking runs of three only along rows: columns count too.
- Forgetting the no-twin rule until the last two rows, when it is the only way forward.
- Counting circles by eye in a long row; the counters beside the grid do it for you.
Where Takuzu comes from
The puzzle was first published in Belgium in 2009 by Frank Coussement and Peter De Schepper, under the name Binairo; Takuzu and binary puzzle are names it carries elsewhere. It has become a staple of puzzle books and daily-puzzle pages, partly because its rules fit in three short sentences.