How to solve Binary Blocks

Put a filled or a hollow square in every empty cell so that each row and each column holds as many of one as of the other.

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

Every cell of a block holds the same square.

Tap a cell for a filled square, tap again for a hollow one, once more to clear it. The squares the board came with stay put: tap one and they all give a shake, to show which they are.

Shown in red: three of the same kind side by side, squares a row or column has too many of, and a block holding both kinds.

A block is two, three or four cells inside an outline: a straight piece of two, a corner of three, a square or a zigzag of four, turned any way. A block does not say what it holds — only that all its cells hold the same. Blocks may touch, and whether two neighbouring blocks are alike or differ follows from the other rules alone.

Two rows or two columns may come out identical — the rules do not forbid it. Every board has exactly one answer, and it can be reached without guessing.

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

Two of the same symbol 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 symbol.

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

As soon as one cell of a block is settled, the whole block is. It is the strongest move in the game: one square turns at once into two, three or four — and any of them may start a new pair.

A block says something before anything stands in it. Two of its cells side by side in one line are a pair only waiting for its square — and a pair cannot have a third of the same next to it. If a square already stands right beside the block, the block must be the other kind.

Blocks that touch may well be alike — the rules do not forbid it. But when one block has two cells side by side in a line and the other carries that line on by a third, they must differ: otherwise three alike would stand there.

When nothing simpler works, read one line whole: try in your head what the block lying in it could hold, and see whether both choices fit the rules. Often one of them gives three alike or a count that does not add up straight away.