What is a Binairo?
Binairo (also called Takuzu or Binary Puzzle) is a logic puzzle in which you fill a grid with two symbols so that no three of the same symbol sit in a row across or down, every row and every column holds equal numbers of each symbol, and no two rows or two columns are identical.
Also known as: Takuzu, Binary Puzzle, Binero.
How do you solve a Binairo?
- 01
Cap every pair
Two of the same symbol side by side, across or down, cannot be joined by a third, so the square at each end of the pair takes the other symbol. Scan the whole board for pairs first; on a fresh eight-by-eight this alone settles a dozen squares.
- 02
Fill the gap in a split pair
Two matching symbols with one empty square between them would make three in a row if the middle matched, so the middle takes the other symbol. Filling a gap often creates a new pair to cap, so alternate the two moves.
- 03
Count the line
Each row and column holds four of each symbol. Once a line has all four of one, every empty square in it is the other. Count before the line looks finished, because the fourth of a kind is easy to place without noticing.
- 04
Place the last few without making a triple
When a line still needs two of one symbol and has three empty squares, ask where they can go without forming three in a row. Often only one arrangement avoids a triple, and a square that would sit in the middle of a triple under every arrangement is decided.
- 05
Compare finished lines with nearly finished ones
Take a complete row and find an incomplete one that matches it everywhere except in two empty squares. If those two must hold one of each symbol, the arrangement that would copy the finished row is forbidden, so the other is right. The site enforces this rule only on complete lines, so seeing it coming is your job.
- 06
Finish with a one-step look-ahead
Every puzzle here has exactly one solution, so guessing is never needed, but the endgame sometimes wants a test: suppose a square holds one symbol, follow the pairs and counts for a move or two, and if that makes a triple or an overfull line, it holds the other.
Common Binairo mistakes
- Thinking equal counts mean alternation. A line can hold a pair of one symbol then a pair of the other; the rule forbids three in a row, not two.
- Checking only rows. The pair you fail to cap vertically is the one that makes a triple three moves later.
- Rejecting two lines for matching before they are finished. Two half-filled rows that agree so far may still diverge; the rule bites only when both are complete.
- Reading the discs as numbers. The filled and hollow discs are only two kinds of same and different, and there is nothing to add up.
Where does Binairo come from?
Binairo was created in Belgium by Peter De Schepper and Frank Coussement and first published in 2009. It became a fixture of newspapers and puzzle magazines in Belgium and the Netherlands and spread from there.
Elsewhere it goes by Takuzu, Binary Puzzle or Binero. Printed versions usually use two colours or the digits nought and one, which is where the “binary” name comes from, though there is no arithmetic in it.
Is Binairo the same as Takuzu?
Yes. Takuzu, Binary Puzzle and Binero are names for the same three rules. Some versions use noughts and ones, some two colours; this site draws filled and hollow discs, and a click cycles a square from empty to one, to the other, and back.
How long does an 8×8 Binairo take?
Most eight-by-eight boards take three to eight minutes once capping and gap-filling are automatic. The daily here is one board of that size, new at midnight UTC, free with no sign-up, and it works on a phone.
Why does Binairo need the no-identical-lines rule?
Without it many boards would have several answers, because the local rules alone leave some pairs of lines free to swap. The rule is what lets a puzzle be set with a single solution, and it is the one rule about the whole board rather than three squares at a time.