How to solve Binario

Fill every empty cell with a zero or a one so that each row and each column holds as many zeros as ones.

Never three alike side by side — not in a row, not in a column.

No two rows read the same, and no two columns do either.

Tap a cell for a zero, tap again for a one, once more to clear it. The digits the board came with stay put.

A reddish cell is one of three alike in a row, or a digit its row or column already has too many of; two lines that read the same are shaded too.

A few digits are given at the start and those stay put; the rest of the cells are empty, and every one of them is yours to fill. Every board has exactly one answer, and it can be reached without guessing — when nothing stands out, there is always some row or some column with only one way left to go.

Two alike side by side is the most common move on the board. A third of the same cannot stand on either side of them — so both neighbouring cells get the other digit. It works the same way in rows and in columns.

Two alike with a single empty cell between them are a pair that does not know it yet. A third of the same in the gap would make a run of three — so the gap gets the other digit.

On a 6 × 6 board every row and every column has exactly three zeros and three ones. A line that already has all its zeros has no choice: every empty cell in it is a one. Pairs and gaps usually leave exactly such tails behind them.

When pairs, gaps and counting have nothing to say, what is left is to read a whole line: how many zeros and how many ones it still lacks, and the ways they can be spread over its empty cells without three alike landing together. A cell that comes out the same in every one of those ways is settled — though no single move pointed at it.

The third rule — no two rows and no two columns are the same — is rarely needed, but on a big board it is sometimes the only way through. A finished line forbids another line of the same kind from ending up identical.