Binary Puzzle
Fill every cell with a 0 or a 1. Never three of the same digit together, an equal count of each in every row and column, and no two rows or columns alike. Tap a cell to cycle it. Every grid here has one answer and can be reasoned out without a single guess.
Also published as takuzu and binairo, and sometimes as tohu wa vohu.
What Is A Binary Puzzle?
A binary puzzle is a square grid holding nothing but 0s and 1s. Some are printed for you; the rest you work out. It looks trivial — two digits, how hard can it be — and the difficulty comes from exactly that, because with only two values every deduction has to come from the arrangement rather than from the digits themselves.
It is a young puzzle. The form spread through European newspapers from around 2009 and is published under several names: takuzu, binairo, and occasionally tohu wa vohu. The rules are identical under all of them.
The Three Rules, And Why The Third One Is Not Optional
| Rule | What it forbids | What you get from it |
|---|---|---|
| No three alike | 000 or 111 anywhere in a row or column | Caps both ends of any pair, and fills any gap between matching digits. |
| Balance | A line with more of one digit than the other | Once one digit is fully placed in a line, every blank in it is the other. |
| No twins | Two identical rows, or two identical columns | Forces a line that nearly matches a finished one to differ. |
The third rule is the one people treat as decoration, and it is the reason these puzzles have single answers at all. Without it a great many grids can be completed two ways — swap a matching pair of rows around and nothing else changes. It is also directly useful: a row with two blanks left that agrees with a finished row everywhere else cannot be filled to match it, so both blanks are settled at once.
How To Open One
- Cap every pair. Two identical digits side by side force the other digit at each end. It costs no thought and it is always available at the start.
- Fill the gaps. A digit, a blank, then the same digit again: the blank takes the opposite. Same rule, seen from the other side.
- Count the line. Half of every line is 0s. As soon as all of one digit is placed, the remaining blanks are all the other — on a twelve-wide grid that is six each.
- Compare with a finished line. Two blanks left, and everything else matching a completed row? Those blanks must break the match.
- Go back to step one. Every digit you place makes new pairs and new gaps. Cycling back is what keeps the puzzle moving; grinding on counting alone stalls.
Sudoku habits get in the way here. Sudoku forbids repeats; a binary puzzle requires them — half of every line is the same digit. Nothing is ever settled by "that digit is already used", which is the reflex most people bring. What settles cells instead is how many are left and what sits next to what.
Sizes Here, And What Changes With Them
The grids run 6×6, 8×8, 10×10 and 12×12, all even because a line cannot hold as many 0s as 1s otherwise. Size changes the puzzle less than the number of givens does: a thinly populated 8×8 is harder than a generous 12×12, because the opening pairs are what get you started and a thinned grid has fewer of them. That is why the families here come in pairs — a generous version and a thinned one at each size — rather than simply getting bigger.
One Answer, And No Guessing — Both Checked
Two separate promises, verified separately because they are different claims. Every grid is confirmed to have exactly one completion. And a solver that only uses the three rules above — never a trial — has to finish it unaided. Digits are removed from a full grid one at a time, and each removal is kept only while both still hold, which is why these carry roughly a quarter of their cells as givens: everything that could go, went.
Binary Puzzle Frequently Asked Questions
What is a binary puzzle?
A grid filled with only 0s and 1s under three constraints: no three of the same digit together in any line, each line holding as many 0s as 1s, and no two rows or columns identical. Also published as takuzu and binairo.
What are the rules of a binary puzzle?
Three, and all three are needed. Never three of the same digit next to each other, across or down. Each row and column holds an equal number of 0s and 1s. And no two rows may match, nor two columns.
What is the first move in a binary puzzle?
Find two identical digits already side by side: the cells at either end must both take the other digit. Then look for a digit, a gap, and the same digit again — the gap takes the opposite one, for the same reason.
Why can no two rows be the same?
It is a rule in its own right, not a consequence of the others, and without it many grids would have two valid answers. It is also useful — a row with two blanks that matches a finished row everywhere else must fill them the other way round.
Are binary puzzles the same as sudoku?
No. Sudoku uses nine digits and forbids repeats; a binary puzzle uses two and requires them, since half of every line is 0s. The reasoning is about balance and runs rather than elimination.
Does every puzzle here have one answer?
Yes, and it is checked rather than claimed. Every grid is verified to have exactly one completion and separately verified to be solvable by reasoning alone. A digit is only removed while both remain true.
Is it free, and does it need an account?
Completely free, no account, no adverts, nothing uploaded. Your progress stays in your own browser.
What else is a binary puzzle called?
Takuzu and Binairo are the two commonest names, and you will also see Binoxxo, Tic-Tac-Logic and Binero. They are all the same puzzle with the same three rules; some versions use crosses and noughts rather than ones and zeros, which changes how it looks and nothing about how it is solved.