Summary: A Binary puzzle — the same puzzle you may know as Takuzu, Binairo, or Unruly — is a square grid you fill with two symbols. Each row and each column ends up half-and-half, and no three identical symbols sit in a line. This guide uses a 6×6 board of 0s and 1s as the worked example; the same rules hold when the pair is letters, colours, or pictures.
Overview
A Binary puzzle starts as an even-sized square with some cells already filled. Those printed cells are givens. Your job is to fill every empty cell with one of the same two symbols so the finished grid obeys two standing rules.
The board on the left is the puzzle: a handful of 0s and 1s, the rest blank. The board on the right is the same grid after every cell is filled. Play along with the smaller labelled pair below.
The Goal
Fill every empty cell with one of two symbols so that:
- No three identical symbols sit in a line — not in a row, not in a column. Two in a row is fine. Three is not.
- Each row and each column is balanced 50/50. On a 6×6 that means three of each symbol. On an 8×8 it means four of each.
Some cells are given. Leave them. A well-formed Binary puzzle has exactly one solution, reached by deduction.
The Rules
- Two symbols only. Classically 0 and 1. The pair can also be two letters, two colours, or two pictures. The solver still reads two states.
- No three in a row or column. If two 1s already sit side by side, the cells on both ends must be 0. If two 1s sit one cell apart, the gap must be 0.
- Equal counts. When a row already holds its full share of 1s, every remaining empty in that row is 0. The same for 0s, and the same down every column.
- Givens stay. A printed cell is part of the answer. Do not change it.
- Unique rows and columns are optional. Some books add one more rule: no two rows match, and no two columns match. It is off unless the book says so. The 6×6 below does not use it — row 1 matches row 4 on purpose.
If you know Sudoku, set it aside here. There are no digits 1 to 9 and no boxes, only two symbols and two rules.
How to Start Solving
Work the left-hand 6×6. Rows and columns are numbered. Cover the right-hand solution and only check at the end.
If you would rather work on paper, copy the givens onto squared paper. A dot is an empty cell.
1 . 1 . . .
. . 1 1 . 0
. . . 1 . .
1 . . . . .
. . 0 . . .
. . . . . 0
Start with a gap between twins. Row 1 already has a 1 in column 1 and a 1 in column 3. If the cell between them were also 1, that would be three 1s in a line. So row 1, column 2 is 0.
Then block both ends of an adjacent pair. Row 2 has 1s in columns 3 and 4. Neither neighbour can be 1. Column 2 is empty, so row 2, column 2 is 0. Column 5 is empty, so row 2, column 5 is 0. Column 6 is already a given 0.
Then finish the count. Row 2 now reads . 0 1 1 0 0. A 6-cell row needs three 0s and three 1s. It already has three 0s, so the last empty — row 2, column 1 — is 1. That row is done: 1 0 1 1 0 0.
The same two moves work down a column. Column 1 now has an adjacent pair of 1s in rows 1 and 2, so row 3, column 1 is 0. That column also holds a given 1 in row 4. Three 1s is the whole column’s quota, so the last two empties are 0: row 5, column 1 and row 6, column 1 are 0.
Another gap, another force. Row 5 now reads 0 . 0 . . .. Two 0s with a gap. The gap cannot be 0. So row 5, column 2 is 1.
Now block down a column. Column 2 has 0s in rows 1 and 2, an adjacent pair. So row 3, column 2 is 1.
Those two moves — block a third-in-a-line, then fill the leftovers when a count is full — solve this 6×6 outright. Keep cycling them on rows and columns until the board is full, then check your finish against the grid on the right. Bigger and harder boards sometimes need one more move: when neither fires, pencil in a symbol and see whether it forces a run of three or an impossible count nearby. If it does, the cell is the other symbol.
If you want these for a book or a site, Puzzle Maker Pro generates Binary puzzles. Try the free demo, see the Binary Puzzles product page, or follow Getting Started with Binary Puzzles.
The Pair You See
The rules never change when the two states are not 0 and 1.
- Numbers — any two digits, when the book is already a number series.
- Letters — A and B, or any two letters. The classic 0 and 1 is just one such pair.
- Colours — two colour shapes, so the page reads as a pattern.
- Images — two pictures: day and night, two animals, two brand marks.
Treat matching pictures exactly like matching digits. Two suns in a row still forbid a third.
Try It Online
In the browser, click a cell to cycle it: empty, then 0, then 1, then back to empty. The printed givens are locked and do not change. The moment you make a run of three, those cells are marked so you can undo the move before it spreads. Counts and matching lines are only checked when you press Verify, so keep tallying as you go. The online boards also use the optional unique rows and columns rule: no two finished rows and no two finished columns may match. Play Binary Puzzles in your browser — nothing to download. The general player controls — verify, reset, the timer, working through a set — are covered once in How to Play Puzzles Online.
Outcome
You can read a Binary grid as two states, stop a third-in-a-line before it happens, finish a row or column when its count is full, and check a finished board: three-and-three on a 6×6, no run of three, givens untouched. Want to make your own? Try the free demo, open the Binary Puzzles product page, follow Getting Started with Binary Puzzles, or browse the Binary Puzzle Tutorials hub.
FAQ
What is a Binary puzzle?
A two-symbol logic grid, also called Takuzu, Binairo, or Unruly. You fill every empty cell so each row and each column holds an equal count of both symbols, and no three identical symbols sit in a line.
How do you start a Binary puzzle?
Look for two identical symbols that already sit side by side or one cell apart. The next cell in that line must be the other symbol. Then look for a row or column that already holds its full share of one symbol — every leftover empty there is the other symbol.
Do two matching rows break the puzzle?
Not on their own. Unique rows and columns is an extra rule some books turn on. It is off by default. The 6×6 on this page has matching rows (row 1 matches row 4) and is still a valid Binary puzzle.
Do I have to use 0 and 1?
No. Any pair works: two letters, two colours, or two pictures. The solver still reads two states. The rules above do not change.
Does every Binary puzzle have only one solution?
Yes. A well-formed Binary puzzle has exactly one solution. Puzzle Maker Pro keeps a board only when logic determines every empty cell.
What sizes do Binary puzzles use?
Even squares from 6×6 to 16×16. A 6×6 is a quick warm-up and a good first board for a class (three of each symbol per line); 8×8 is the everyday size (four of each); 16×16 is the big one. Puzzles also come in Easy and Hard. Each row and column always splits 50/50, so the side length stays even.