Binairo Puzzles
Fill every square with one of two symbols so no three alike ever sit in a line.
Hints available. Play as many boards as you like.
Ready when you are.
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Scan for the same board — no hints.
How to play
Every square holds one of two symbols: a circle or a square. Tap a square to cycle it from empty to circle to square and back. The symbols differ by shape rather than color, so nothing depends on being able to tell two hues apart.
Three rules govern every board. No three identical symbols may sit next to each other in a row or a column. Each row and each column must end with exactly as many circles as squares. And no two rows may be identical, nor any two columns.
The squares printed in dark are given and cannot be changed. Everything you place appears in violet, so you can always see which decisions are yours.
Strategy
Start with the pairing rule. Wherever two identical symbols already sit side by side, the squares at either end of that pair must both be the opposite symbol — otherwise you would have three in a row. This single deduction usually opens a board.
Then look for the sandwich. A gap between two identical symbols, as in circle-blank-circle, must be filled with the opposite symbol for the same reason. Sweep every row and column for both shapes before doing anything harder.
When those run dry, count. If a row already holds half its squares as circles, every remaining square in that row is a square, with no further reasoning needed. The balance rule finishes far more lines than people expect.
Difficulty and variants
Easy uses a 6x6 grid with generous givens; medium moves to 8x8; hard is a 10x10 board with the fewest starting squares. The grid grows, but the real difference is how far you must chain the three rules before a square becomes certain.
Questions, answered
What is a binairo puzzle?
A grid filled with two symbols under three rules: never three alike in a line, an equal count of each per row and column, and no two identical rows or columns. It is also sold as Takuzu, Binary Puzzle or Unruly.
Is binairo the same as Takuzu?
Yes. Binairo, Takuzu, Binary Puzzle and Unruly all describe the same puzzle; the names come from different publishers.
Can a binairo be solved without guessing?
Every board here is generated and then checked to confirm it has exactly one solution reachable by the rules, so trial and error is never required.
Why can't two rows be the same?
It is the third rule, and it is what makes the endgame interesting: two rows that have become identical tell you one of them is wrong even before you find the offending square.