How to solve the one-star puzzle

Place stars so that every row, every column and every outlined region holds exactly one 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 its star there — and that star is the line’s one star, 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 placed is a row, a column and a region settled, and eight neighbours ruled out. Most boards fall to nothing more than this — each star crosses out cells, and the crossings leave the next region with one place to go.

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

Counting a row, a column or a region says where its star can go — and also what that star will touch. If every cell it could stand on 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.