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How to Solve Binairo: 5 Techniques That Work

To solve Binairo, work one row or column at a time. Three quick checks do most of the work: two alike side by side (the squares at either end are the other colour), two alike with a gap between them (the gap is the other colour), and a line that already has half of one colour (the rest is the other). When those run out, two more techniques finish the job: lines that mustn’t copy another, and listing every way a line could still be filled.

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New to Binairo? Read the Binairo rules first. This page assumes you know the three rules: no three alike side by side, half of each colour in every line, and no two lines the same.

1. Pairs

Two alike side by side can’t have a third beside them, so the squares at either end of a pair are the other colour.

Pairs: two teal side by side A row of six with teal in squares 3 and 4. The squares at either end of them, 2 and 5, must be yellow. 1 2 3 4 5 6 1
Two teal side by side, in squares 3 and 4: squares 2 and 5 must be yellow.

2. Gaps

Two alike with one square between them would make three in a row if that square matched, so the square between them is the other colour.

Gaps: one square between two yellow A row of six with yellow in squares 2 and 4. The square between them, 3, must be teal. 1 2 3 4 5 6 1
Yellow in squares 2 and 4: square 3 must be teal.

3. Full count

Every line is half and half. Once a line has half of one colour, every other square in it is the other colour.

Full count: a row with its three teal A row of six: teal, yellow, teal, empty, empty, teal. That's three teal, half the row, so the two empty squares, 4 and 5, are yellow. 1 2 3 4 5 6 1
Teal in squares 1, 3 and 6 is half the row, so squares 4 and 5 are yellow.

4. No repeats

When a line has just two squares left, one of each colour, and a finished line runs the same way and matches it everywhere else, filling the two squares the way that line has them would copy it. So they go the other way round.

No repeats: two squares left, and a row to avoid copying Two rows of six. The first is complete: yellow, teal, teal, yellow, teal, yellow. The second matches it in its first four squares, with squares 5 and 6 left: one of each colour. Teal then yellow would copy the first row, so it's yellow then teal. 1 2 3 4 5 6 1 2
The bottom row matches the top one in its first four squares. Teal then yellow would copy it, so squares 5 and 6 are yellow then teal.

5. Every arrangement

When nothing quicker works, pick a line with only a few squares left and try each way it could be finished, keeping the rules. A square that comes out the same in all of them is settled.

Every arrangement: the only way to finish a row A row of six: yellow, empty, empty, teal, empty, yellow. It needs one more yellow and two more teal. Yellow in square 2 would force teal in squares 3 and 5, making three teal in a row, so square 2 is teal; then square 3 must be yellow, or squares 2 to 4 would be three teal, and square 5 is teal. 1 2 3 4 5 6 1
Yellow, two empty squares, teal, an empty square, then yellow. Only one way works: teal, yellow, teal, teal.

In this row, square 2 can’t be yellow: the row would then need teal in both squares 3 and 5, and squares 3 to 5 would be three teal. So square 2 is teal. Then square 3 can’t be teal (squares 2 to 4 would be three teal), so it’s yellow, and square 5 is the last teal.

This is slower, but it always finds whatever one line can tell you, including the no-copying rule. It’s the technique to reach for when you’re stuck.

How often each technique is needed

We solved every one of the game’s 150 levels by following the hints, which always use the simplest technique that works. This is how many times each technique was used, on average, per level:

Technique Easy 6×6 Medium 8×8 Hard 10×10
Pairs 8.6 15.2 26.1
Gaps 4.8 8.5 11.7
Full count 8.5 8.5 11.0
No repeats 0 1.2 1.2
Every arrangement 0 4.7 8.0

Pairs, gaps and the full count do most of the work at every size, and they’re all an Easy level needs. No repeats is needed on 41 of the 50 Medium levels and 38 of the Hard ones; every arrangement on 49 Medium levels and all 50 Hard.

An 8×8, solved in three stages

This is Medium level 2 from the game: an 8×8 with 14 clues.

Medium level 2 from the game An 8 by 8 Binairo with 14 clues, before it's started. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Medium level 2, before you start.

Stage 1: the quick techniques

Fifteen steps of the three quick techniques come first: 8 pairs, 5 gaps and 2 full counts. Then they run dry: no line has a pair, a gap or a full count left to use.

After the first 15 steps Medium level 2 after 15 steps of pairs, gaps and full counts. Nothing simpler is left: the next step needs the no-repeats rule. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
After 15 steps, the quick techniques have nothing left.

Stage 2: no repeats, then every arrangement

Row 2 reads yellow, two empty squares, then teal, yellow, yellow, teal, teal. It needs one more of each colour. Row 7 is finished, and matches row 2 everywhere except those two squares, where it has teal then yellow. Row 2 can’t copy it, so it gets yellow then teal.

Step 16: no repeats Row 2 has two squares left, one of each colour, and matches a finished row everywhere else. Filling them that row's way would copy it, so they go the other way round. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Row 2 (and row 7, the row it mustn’t copy) highlighted: its two empty squares go yellow, teal.

Column 4 comes next. It has three squares left, in rows 5, 6 and 8, and needs two yellow and one teal for them. Only two ways keep the line rules, and one of them would make column 4 the same as column 7, which is already finished. That leaves one way: teal in row 5, yellow in rows 6 and 8.

Step 17: every arrangement on column 4 Column 4 has three squares left, in rows 5, 6 and 8. Two ways of filling them keep the line rules, but one would copy column 7, so the other is the only way: teal in row 5, yellow in rows 6 and 8. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Column 4: of the two ways to finish it, one would copy column 7.

Stage 3: quick techniques to the end

Those squares are enough. Nineteen more quick steps finish the grid (7 pairs, 5 gaps and 7 full counts) without needing anything harder again.

Medium level 2, solved The finished 8 by 8 grid: four of each colour in every row and column, no three alike side by side, and no two rows or columns the same. 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
Medium level 2, solved.

When you get stuck

  • Look at the lines you’ve just changed. Every new square changes a row and a column, and the next move is usually on one of them.
  • Count every line. A line with half of one colour finishes itself, and it’s easy to miss once the grid fills up.
  • Compare nearly finished lines with finished ones. Two squares left, one of each colour, and a finished line that matches the rest: that’s a no-repeats move.
  • List the arrangements on a nearly finished line. With only a few squares left in a line, there are only a few ways to fill it.
  • Don’t guess. Every puzzle here can be finished one line at a time.

Next steps

Questions

What's the first thing to look for?

Two alike side by side, and two alike with one square between them. Both settle squares on the spot, and every one of the game’s 150 levels has at least one to start from.

When do I need the harder techniques?

Not on Easy: every Easy level finishes with pairs, gaps and the full count. On the game’s Medium levels, every arrangement is needed about 5 times per puzzle, and on Hard about 8.

Is it ever right to guess?

Not on PeerPuzzles. Every puzzle here can be finished one row or column at a time, so there’s always a line where something is certain.