Binary Puzzle (Takuzu / Binairo)

Binary Puzzle (also called Takuzu or Binairo) is played on an even-sided square grid where you fill every cell with a 0 or a 1 while obeying three rules at once: no three of the same value in a line, an equal count of 0s and 1s in each line, and no two identical rows or columns. Some cells come filled in as givens to start you off.

What are the three rules of Binary Puzzle?

The first rule is the no-three-in-a-row rule: you may never place three of the same value consecutively in any row or column, so neither 0 0 0 nor 1 1 1 is ever allowed. The second is the balance rule: each row and each column must contain an equal number of 0s and 1s — on a 6×6 grid that means exactly three of each in every line. The third is the uniqueness rule: no two rows may be identical, and no two columns may be identical.

Why does every board have exactly one solution?

Those three constraints are enough to force a single answer. Because each cell is one of only two values and every rule is a hard logical limit, every board on this page is generated and checked to have exactly one solution reachable by reasoning alone. You never have to guess: there is always a cell whose value is forced by the rules already in play.

To solve a binary puzzle, play forced moves first: a pair of equal cells forces the opposite value on each side, a single gap between two equal cells forces the opposite value in the middle, and a line that already holds all its 0s (or 1s) must be completed with the other value.

Which binary puzzle techniques should you learn first?

A handful of reliable moves crack almost any board. These are the core binary puzzle rules of thumb worth learning first:

• The pair. Whenever two equal cells sit side by side — say 1 1 — the cell on each side must be the opposite value, here a 0, otherwise you would make three in a row.
• The gap. When two equal cells have a single empty cell between them, like 1 _ 1, the middle must be a 0; a 1 there would create 1 1 1.
• The count. Once a row (or column) already holds all of its 0s — three of them on a 6×6 — every remaining empty cell in that line must be a 1, and the same the other way round.
• Avoid duplicates. If a row is one cell from completion and the only way to fill it would copy an already-finished row, the uniqueness rule forbids it, so the cell takes the other value.

What is the winning habit when solving Takuzu?

The winning habit is to play every forced move first and let each new digit reveal the next. Scan for pairs and gaps, top up any line that is nearly balanced, and never guess — a proper Takuzu always has a provable next cell.

The single most important binary puzzle technique is never allowing a third matching value in a line: two equal cells together (a pair) force the opposite value on each side, and two equal cells one apart (a gap) force the opposite value in the cell between them. If you learn one technique for how to solve binary puzzles, make it this one — most early progress on any board comes from it.

How do the pair and gap patterns work?

The technique has two shapes. The first is the pair: any time you see two of the same value together, such as 0 0, the cells immediately to either side are forced to the opposite value. Place a 1 on each end of that pair and you have two free deductions. The second is the gap: when the same value sits two apart with one empty cell between them — the pattern 0 _ 0 — the middle cell cannot match, so it must be a 1.

Why does one deduction cascade across the grid?

Work both patterns in rows and columns alike, because the no-three rule applies in every direction. Each forced cell you place often creates a new pair or gap nearby, so a single deduction tends to cascade across the grid. Keep sweeping the board for these shapes and a surprising number of cells fill themselves in before you have done any harder thinking at all.

A short run on a 6×6 row shows the rhythm: a leading 1 1 pair forces a 0 beside it, a 0 _ 0 gap forces a 1 in the middle, and once the row holds all three of its 0s the balance rule fills the rest with 1s — never a guess.

How does the pair force the first cell?

Suppose a row reads 1 1 _ _ _ _ . The opening 1 1 is a pair, and since the cell to its left is the grid edge, the no-three rule forces a 0 into the third cell: the row becomes 1 1 0 _ _ _ .

How do the gap and balance rules finish the row?

Now look further along and imagine the row has developed into 1 1 0 _ 0 _ , with a 0 two cells apart. That is a gap — the empty cell between the two 0s must be a 1 to avoid 0 0 0 — giving 1 1 0 1 0 _ . At this point the row already contains its three 0s, so the balance rule takes over: the last empty cell can only be a 1, completing the line as 1 1 0 1 0 1, with three of each value.

That single completed row now constrains every column it crosses, and a glance at the uniqueness rule confirms no other finished row may copy it. Each forced cell trims the choices around it, and the solution grows outward from the certainties — never a guess required.

This page offers Binary Puzzle at two even-sided sizes — a friendly 6×6 (three 0s and three 1s per line) and a meatier 8×8 (four of each per line) — with difficulty scaling by size and by how many cells are given at the start. Binary grids are always even-sided, because each row and column has to split exactly in half between 0s and 1s — an odd length could never balance.

• The 6×6 board needs three 0s and three 1s per line. It is ideal for learning the pair, gap and balance moves, since the whole grid stays comfortably in view.
• The 8×8 board needs four of each per line. The longer rows give the no-three and uniqueness rules more room to bite, so you plan a little further ahead before committing a value.

Difficulty scales with size and with how many cells are given at the start: fewer givens mean longer chains of deduction before the grid locks in. Tap New for a fresh board at either size, or play the shared Daily to solve the same puzzle as everyone else that day.

This puzzle travels under several names — most commonly Takuzu and Binairo (from the word “binary”), and also Binary Sudoku, Tohu wa Vohu, and the slightly relaxed variant Unruly — but they are all the same grid of two symbols governed by the no-three, balance and uniqueness rules. Any tip here carries straight across.

At heart this is a grid-filling logic puzzle, which makes it kin to other deduction puzzles in this collection. If you enjoy filling a grid by pure reasoning, try Sudoku, where each row, column and box holds the digits 1 to 9 once, or Nonogram, where number clues tell you which cells to fill. The forced-move, never-guess discipline transfers directly between all three.

A few words come up whenever Binary Puzzle is discussed — cell, given, pair, gap, balance and uniqueness — and knowing them makes any guide easier to follow.

• Cell — a single square in the grid, holding a 0, a 1, or nothing yet.
• Given — a cell already filled in at the start as a clue; you cannot change it.
• Pair — two equal values side by side, which force the opposite value on each side.
• Gap — two equal values with one empty cell between them, forcing the opposite value in the middle.
• Balance — the rule that each row and column holds equally many 0s and 1s.
• Uniqueness — the rule that no two rows, and no two columns, may match.

You don’t need the jargon to play — just tap a cell to cycle empty → 0 → 1 — but it makes guides easier to follow.

Most Binary Puzzle tangles trace back to a few habits: guessing a value, losing track of each line’s balance, ignoring the column rules, overlooking uniqueness, and skimming past the 1 _ 1 gap.

• Guessing a value. An unjustified 0 or 1 can sit happily for a while before clashing with a rule far across the grid. Find the forced cell instead.
• Forgetting the balance. It is easy to focus on avoiding three in a row and overshoot a line’s share of 0s or 1s — keep a running count for each row and column.
• Ignoring columns. Every rule applies vertically as well as horizontally; a move that is fine in its row may still break its column.
• Overlooking uniqueness. Two rows (or columns) that end up identical mean an error earlier, even if no three-in-a-row appears — this rule is part of the solve, not an afterthought.
• Missing the gap. The 1 _ 1 pattern is easy to skim past; train your eye to spot values two cells apart, not just adjacent ones.

Binary Puzzle has a clean, almost meditative appeal — only two symbols and three rules, no arithmetic and no luck — yet enough depth to keep you thinking as you spot the pair, the gap and the balance and watch the grid resolve. A 6×6 board is a tidy few-minute solve; an 8×8 is a longer, more absorbing puzzle for when you want to settle in.

Like the rest of this collection it is fair by design: every board has a single answer you can reach by reasoning, so progress always feels earned rather than lucky. Playing the shared Daily gives you the same grid as everyone else and a small streak to keep. And because Binairo trains pattern-spotting and step-by-step deduction, it pairs naturally with the other grid puzzles here — once you enjoy filling cells by logic, Sudoku and Nonogram are an easy next step.

Binary Puzzle is a modern creation rather than a classic pencil puzzle, rising to popularity from around 2009 onward — carried by newspapers, puzzle books and mobile apps that suited its simple two-symbol grid perfectly — and picking up names like Takuzu, Binairo, Binary Sudoku, Tohu wa Vohu and the looser Unruly along the way.

As it spread it picked up a clutch of names. It is widely known as Takuzu and as Binairo — the latter taken straight from the word “binary” — and you will also see it billed as Binary Sudoku or Tohu wa Vohu, with a looser variant published as Unruly. The names differ, but the heart of it never changes: a grid of 0s and 1s, the no-three, balance and uniqueness rules, and a single answer reachable by pure logic — no arithmetic, no guessing, just careful reading of the board.