What are the rules of a binary puzzle?
A binary puzzle is a grid you fill with 0s and 1s by three rules. Never put three of the same digit next to each other, across or down. Give every row and every column as many 0s as 1s. And make no two rows the same, and no two columns the same. Some cells are filled in at the start; the rules decide the rest.
Pick a 6 × 6 or 8 × 8 grid. A tap changes a cell from empty to 0 to 1 and back; on a keyboard, the arrows move and 0, 1 and Backspace write. A broken rule is outlined in red as soon as it happens, worked out from the grid alone.
How is your Binary Puzzle time calculated?
Your result is the time from Start until the grid is full and keeps every rule. Beside it are the times you pressed Check (which marks any cell that disagrees with the answer) and Hint (which fills in one cell, or fixes a wrong one). There is no rating, because no published typical time exists for puzzles built like these.
A 8 × 8 grid takes far longer than a 6 × 6, and two puzzles of the same size can differ a lot. Tapping on a phone is a little slower than typing, and the clock runs while you think.
How do you solve binary puzzles?
- Pairs. Two of the same side by side? The cells on both ends of the pair must be the other digit, or there would be three in a row.
- Gaps. Two of the same with one empty cell between them? The middle must be the other digit.
- Counting. Once a line of 6 has 3 of one digit, every empty cell in it takes the other.
- Finishing lines. When a line has two cells left and they could go either way, compare it with the finished lines: the rows must all be different, so one order is usually ruled out.
It also helps to know how few lines are allowed at all. Only 14 rows of 6 keep the first two rules, and only 34 rows of 8, so a half-filled line often has only one way to finish.
Can every Binary Puzzle be solved without guessing?
Yes. Each puzzle starts as a complete grid. Cells are then emptied one at a time, in random order, and a cell stays empty only if a solver that never guesses can still fill the whole grid. It reasons line by line, listing every way to finish a row or column within the rules. At least 12 cells stay filled on a 6 × 6 and 22 on a 8 × 8, so a puzzle is a few minutes' work rather than an hour's. The site's tests check hundreds of puzzles and count their answers by brute force: always exactly one.
The code also counts every complete 6 × 6 grid that keeps all three rules: there are 4,140 of them (72 for a 4 × 4).
Is this the same as Takuzu or Binairo?
It is the same kind of puzzle. Binary puzzles are published under many names; Takuzu and Binairo are two of the best known, and both are trademarks, which is why this page uses the plain name. Some versions use colours or X and O instead of 0 and 1; the rules are the same.
For another grid of yes-or-no choices, try Star Battle; for one where every press changes its neighbours, Lights Out.