How to solve Binairo – rules and strategies

What is Binairo?

Binairo is a logic puzzle played on a square grid, usually 6×6, 8×8 or 10×10. Each cell holds one of two symbols – traditionally 0 and 1, which is why it is also called a binary puzzle or Takuzu. In Nordgrid the two symbols are a sun ☀ and a snowflake ❄.

The rules

1. No more than two in a row. Three of the same symbol may never sit next to each other, horizontally or vertically.
2. Balance. Every row and every column has the same number of each symbol – three and three in a 6×6 grid, four and four in 8×8.
3. Clues between cells (Nordgrid). An = between two cells means they are the same; an × means they are different.

In classic Binairo there is often an extra rule: no two rows or columns may be identical. Nordgrid’s sun-and-snow version leaves that rule out and uses = and × clues instead – every puzzle still has exactly one solution.

Technique 1: Pairs

When two of the same symbol sit side by side, the cells at both ends must be the other symbol – otherwise you would get three in a row.

?☀☀? → ❄☀☀❄

Technique 2: Gaps (the sandwich)

When two of the same symbol have exactly one empty cell between them, that cell must be the other symbol.

❄?❄ → ❄☀❄

Technique 3: Counting

When a line already has its full share of one symbol, every remaining empty cell must be the other one. In a 6×6 grid, a row with three suns gets snow in all its empty cells.

☀☀☀ → ☀❄☀☀❄❄

Check it: no three suns sit together, and there are three of each. Counting is the technique that finishes most lines.

Technique 4: Using = and ×

The clues work like pairs and gaps in disguise. If one cell of an = pair is a sun, the other is a sun too. An × pair always holds one of each – so it counts as one sun and one snowflake in that line, which makes counting much easier.

A powerful trick: a row of six with two × pairs already contains two suns and two snowflakes. The two remaining cells must then be one of each as well.

Technique 5: Ruling out the impossible

When a line needs only one more of a symbol, try that symbol in each empty cell in your head. If one placement would force three of the other symbol in a row, that cell is ruled out.

Take a row of six with snow in the first and fifth cells: ❄❄. It needs one more snowflake and three suns. If the last cell were snow, the three cells in the middle would all have to be suns – three in a row, which is not allowed. So the last cell must be a sun:

❄❄ → ❄❄☀

This is the technique that cracks most hard and expert puzzles. It feels like trial and error at first, but it is pure logic: you only look one step ahead and never fill in a cell you are unsure of.

A good order to work in

1. Scan for clues first. Fill every cell an = or × clue settles directly.
2. Then pairs and gaps. Sweep every row, then every column. These two techniques alone often fill a third of the grid.
3. Count. Look for lines that already have their full share of one symbol.
4. Repeat. Each new cell can create new pairs and gaps, so go round again.
5. Only then rule out. Use technique 5 on lines with few empty cells left.

Common mistakes

• Forgetting the columns. It is easy to solve row after row and miss a column that already has three suns.
• Miscounting in big grids. In a 10×10 grid each line needs five of each. Count twice before you fill a whole line.
• Guessing to “see what happens”. A wrong guess can sit unnoticed for many moves. If you are unsure, find another cell – there is always a logical next move.

When you get stuck

• Look for “almost full” lines. A line missing only two or three symbols often has just one legal way to finish.
• Try both options – in your head. If placing a sun in a cell would force three in a row somewhere else, the cell must be snow. This is logic, not guessing.
• Switch direction. After a few moves in rows, scan the columns. New pairs and gaps appear all the time.
• Take a hint. In Nordgrid a hint shows the next logical move and explains which technique it uses.

Practice every day

Binairo gets fast once the four techniques become automatic. Start with 6×6 grids, move on to 8×8 and try 10×10 when the patterns jump out at you. A short puzzle every day is the best way to improve.