How to solve Star Battle

Place stars so that every row, every column and every outlined region holds exactly two of them.

No two stars may touch, not even at a corner.

Crosses are your own notes of where a star cannot go; only the stars are the answer.

Tap a cell to cross it out, tap again for a star, once more to clear it. Drag across cells to cross out several at once.

A star turns red when it touches another, or when its row, column or region holds too many.

Nothing is given: the board starts empty, and every star is yours to place. The crosses are the other half of the game — a cell crossed out is a cell you no longer have to think about, and most of solving is crossing out until the stars have nowhere else to be. Every board has exactly one answer, and it can be reached without guessing.

A region that fits inside a single row or column has to put both of its stars there — and they are that line’s two stars, so nothing else in the line can be one. It reads both ways round: a line that belongs entirely to one region says just as much. It is the opening move on nearly every board, and it needs no star to be placed first.

A star rules out the eight cells around it, and that is the whole of what one star does here: the row, the column and the region it stands in are each still waiting for a second. What closes a line is its second star — and then everything still open in it goes at once. Most boards fall to nothing more than this, and to the counting the crossings keep making possible.

Two rows hold four stars between them. If two whole regions lie inside those rows, those regions supply all four — and no other region can put a star there. The single-line move above is this argument with one line and one region; it works with any number of them, and with columns just the same.

A region’s shape is a count of its own: a 2 × 2 block can hold one star at most, and so can any three cells that all touch one another. A region shaped like a bent stick has room for two stars in only one or two ways.

Counting a row, a column or a region says where its stars can go — and also what they will touch. If every way of placing them touches the same cell outside, that cell can never be a star, and it is crossed with nothing placed. It is the what-if — suppose a star here, and watch a line or a region run out of room — asked from the line’s side, where it is a count rather than a guess: one row, column or region at a time is the whole technique, and a supposition that needs a second one is guessing.