Play Binary (Takuzu) Online
Fill every cell with a 0 or 1. No three in a row, equal counts per line, and every row & column must be unique. Five grid sizes and three difficulty levels.
Created by Brian Hamilton
Click a cell to place 0 or 1
How to play Takuzu
Fill every cell with a 0 or a 1 so that all three rules hold.
- No three in a row. Never three of the same digit next to each other, in any row or column.
- Balance. Every row and every column holds the same number of noughts as ones — half each.
- No repeats. No two rows may be identical, and no two columns may be identical.
- Every puzzle has exactly one solution and never needs a guess.
Controls: click a cell to cycle it through 0, 1 and blank. Grey digits are given and cannot be changed. Check highlights mistakes.
Three rules that compound
Takuzu has only three rules, and each looks mild on its own. What makes the puzzle work is how sharply they multiply together.
A row of ten cells can be filled with noughts and ones in 1,024 ways. Ban runs of three and 178 survive. Require five of each digit instead and 252 survive. Apply both and you are down to 84.
| Row length | Possible rows | No run of three | Balanced | Both |
|---|---|---|---|---|
| 6 | 64 | 26 (41%) | 20 (31%) | 14 (22%) |
| 8 | 256 | 68 (27%) | 70 (27%) | 34 (13%) |
| 10 | 1,024 | 178 (17%) | 252 (25%) | 84 (8%) |
Notice the direction of travel. As the grid grows, each rule individually lets through a smaller share, and the two together shrink faster still — from 22% of rows at six wide to 8% at ten. Bigger Takuzu grids are not proportionally harder; the constraints tighten as they grow.
The third rule — no two rows alike, and no two columns alike — then removes a handful more. It is the rule people forget, and it is usually what settles the last two ambiguous lines at the end of a puzzle.
Two patterns do most of the solving
Almost every move in Takuzu comes from one of two shapes. Both follow directly from the no-three-in-a-row rule, and both are worth training your eye to spot without thinking.
Those two cover the local deductions. The third source of moves is counting: once a row holds half its cells as ones, every remaining cell in that row is a nought, and vice versa. On a 6×6 that means three of a digit closes the row out.
Worth checking against the rules yourself: in a row of six starting 1 1, only two complete rows exist. Starting 1 1 . 1 or 1 1 0 0, only one does — the row is finished the moment you spot it.
A worked board
Here is a 6×6 from the generator on this page, with half its cells filled in.
The top row reads 0 0 1 1 0 with one cell blank, and it shows both patterns
at once: the 0 0 pair is why the third cell is a 1, and the
1 1 pair is why the fifth is a 0. The last cell needs no pattern at all
— the row already holds three noughts, which is all a row of six may have, so what is
left must be a 1.
Where solvers get stuck
Working only along rows. Both line rules apply to columns exactly as they do to rows, and columns are where most people leave deductions on the table. After filling anything, look down as well as across.
Forgetting the counting rule until the end. The pair and sandwich patterns are visual and get spotted; the “this row already has three ones” deduction is arithmetic and gets missed. It is often the faster of the two.
Never using the no-duplicate-lines rule. It only bites late, when two lines are nearly complete, but at that point it is frequently the only thing that resolves them. If you are stuck at the very end with two rows that could go either way, compare them with the rows you have already finished.
Two things you can check about these puzzles
Every puzzle has exactly one solution, and it is verified cell by cell. Each board starts as a complete valid grid. Cells are then blanked one at a time, and a cell is only left blank if a solver confirms the puzzle still has a single answer — otherwise the digit goes straight back. Because the process starts from a finished grid and never takes a step that introduces ambiguity, a second solution can never creep in.
Difficulty is simply how many cells are removed, and the proportion is fixed. The generator aims to blank 35% of the grid on Easy, 50% on Medium and 62% on Hard. That leaves roughly 67%, 50% and 39% of cells showing, and it holds at every size — on a 6×6 that is about 24, 18 and 14 of the 36 cells. Count the filled cells on a fresh board and you can tell the difficulty without looking at the setting.
Takuzu, Binairo and Unruly
The same puzzle circulates under several names. Takuzu and Binairo are the most common, and you will also meet Unruly, Binary Puzzle and Tohu wa Vohu. Some versions use black and white circles rather than noughts and ones, which changes nothing about the logic.
It shares the no-repeats-in-a-line feel of Sudoku but works on a completely different footing: only two symbols, and rules about runs and totals rather than about which values are missing.
More logic puzzles
If you like puzzles with only two states per cell, try these: