Binairo is also called Takuzu, Binary Puzzle or Binero. Simon Tatham's puzzle collection has a close version called Unruly, with black and white squares. The phone game 0h h1 uses the same rules with red and blue tiles.
In Quirk, a 0 is a ring and a 1 is a disc with a slot. On this page, we simply write 0 and 1.
The rules
- Fill every box with 0 or 1.
- Never put 3 of the same together, across or down. Two side by side is fine.
- Each row and column needs as many 0s as 1s.
- No two rows may be the same, and no two columns may be the same.
- A row may match a column.
- Some boxes start with a 0 or 1. You cannot change those.
Some versions of the puzzle leave out the rule about different rows and columns. Quirk always uses it.
A worked example
Here is a small board with 4 rows and 4 columns. Each row lists its boxes from left to right.
- Row 1: empty, 0, 0, empty.
- Row 2: 0, 1, empty, 1.
- Row 3: 0, empty, empty, empty.
- Row 4: all four boxes are empty.
- Row 1 has two 0s side by side. A third 0 next to them is not allowed. So both ends of row 1 take a 1.
- Row 2 already has two 1s. That is half of its four boxes. So its empty box takes a 0.
- Column 1 now reads 1, 0, 0 from the top. It already has two 0s, so the bottom box takes a 1.
- Column 3 starts with 0, 0. It still needs two 1s, so both boxes below take a 1.
- Column 4 starts with 1, 1. So both boxes below take a 0.
- Row 3 now reads 0, empty, 1, 0. It needs one more 1, so the empty box takes a 1.
- Row 4 now reads 1, empty, 1, 0. It needs one more 0, so the empty box takes a 0.
- Now check the board. The rows read 1001, 0101, 0110 and 1010. No two rows match, and no two columns match. The board is solved.
Here is a second, shorter example about different rows. Row 1 of a small board is finished: 0, 0, 1, 1. Row 2 reads 0, empty, empty, 1.
- Row 2 still needs one 0 and one 1.
- There are two ways to fill it: 0, 0, 1, 1 or 0, 1, 0, 1.
- The first way would copy row 1, and that is not allowed.
- So row 2 must be 0, 1, 0, 1.
Beginner techniques
Pairs
Look for two matching numbers side by side. The boxes just before and after them take the other number. So 1, 1 gets a 0 on each side.
Gaps
Look for one empty box between two matching numbers. It takes the other number. So 0, empty, 0 becomes 0, 1, 0.
Half and half
Count the 0s and 1s in a row or column. Once half the boxes hold the same number, fill every empty box with the other number.
Count what is left
Sometimes pairs and gaps do not help. Then count what a row still needs, and try where it fits.
Take a row of six: empty, empty, empty, 0, 1, 1. It still needs two 0s and one 1. If the 1 went in box 1, boxes 2, 3 and 4 would all be 0. That is 3 together, so box 1 takes a 0.
Look for copies
When a row is nearly done, compare it with the finished rows. If one way to fill it copies a finished row, use the other way. Do the same with columns.
Common mistakes
- Checking the rows but forgetting the columns.
- Putting 3 of the same in a column because you only looked across.
- Counting wrong. In a row of 8 boxes, half is 4.
- Thinking a row may not match a column. It may.
- Guessing. Every box can be worked out, so look for a sure box instead.
Questions
Is Binairo the same as Takuzu?
Yes. Takuzu, Binary Puzzle and Binero are other names for the same puzzle. Some versions leave out the rule that rows and columns must differ. Quirk keeps that rule.
Is Binairo the same as LinkedIn's Tango?
They are close cousins. LinkedIn's Tango uses suns and moons on a 6 by 6 grid. It has the same rules about 3 together and half and half. Tango also puts = and × signs between boxes. An = sign means the two boxes match, and × means they differ. Tango does not ask for different rows.
What sizes are there in Quirk?
Quirk has boards of 4 by 4, 6 by 6, 8 by 8 and 10 by 10. A bigger board is not always harder. Harder boards ask for cleverer steps.
Does every puzzle have one answer?
Yes. Each board has exactly one answer. You can always reach it with the rules, without guessing.
What if I get stuck?
Ask for a hint. Quirk marks the boxes that matter and tells you which rule to use. You can also undo a move or reset the board.
Is Binairo good for beginners?
Yes. Small boards only need pairs, gaps and counting. Short lessons in Quirk show each idea on a board first.
Related puzzles
Playing it in Quirk
Tap a box for a ring, which is 0. Tap again for a disc with a slot, which is 1. Tap once more to clear the box.
Drag across boxes to give them all what the first box gets. Boxes that look deeper hold given pieces, and you cannot change them.
