How to solve Binairo: pairs, sandwiches and counting
5 min read ·
Binairo (also known as Takuzu or the binary puzzle) fills a grid with only two symbols: 0 and 1, shown as white and black. Three simple rules decide every cell, and once you know the patterns they make, the grid fills itself in a steady rhythm.
This guide goes through the patterns from the most common to the rarest.
The rules
- Fill every cell with a 0 (white) or a 1 (black).
- No three of the same symbol in a row, across or down.
- Every row and every column has as many 0s as 1s.
- No two rows are the same, and no two columns are the same.
Pairs and sandwiches
These two patterns solve most of the grid:
- Pair: two equal symbols side by side (0 0) must have the other symbol on both ends: 1 0 0 1.
- Sandwich: a gap between two equal symbols (1 _ 1) must be the other symbol: 1 0 1.
Counting to half
Each row of an 8×8 grid holds exactly four 0s and four 1s. Once a row has four of one symbol, every empty cell left in it is the other symbol.
Counting also works earlier. If a row needs one more 1 and has three empty cells, look at where that 1 can go without making three in a row: often only one position works, and the rest are 0s.
No two rows alike
This rule matters near the end. When a row has only two empty cells left and it would match a completed row if you filled them one way, you must fill them the other way. Compare almost-finished rows with completed ones, and do the same with columns.
A solving routine
- Fill every pair's ends and every sandwich's middle.
- Complete any row or column that has half of one symbol.
- Where a line needs only one more of a symbol, see where it fits without three in a row.
- Near the end, compare nearly full lines with finished ones to avoid duplicates.
Practise
Puzzimo's Binairo comes in 6×6, 8×8 and 10×10; the daily challenge is 8×8, and every puzzle has exactly one solution. Tap a cell to cycle white, black and empty, or pick a tool with the keys 1 to 3 and paint by dragging. Undo is free.
Frequently asked questions
Is Binairo the same as Takuzu?
Yes. Binairo, Takuzu, binary puzzle and Binero are names for the same puzzle with the same three rules.
What's the first thing to look for in Binairo?
Pairs and sandwiches. Two equal symbols side by side force the other symbol on both ends, and a gap between two equal symbols must be the other symbol.
When does the 'no identical rows' rule help?
Mostly at the end. When a row has two empty cells and one way of filling them would copy a finished row, the other way is the answer.