How to solve Star Battle

Place stars so that every row, every column and every outlined region holds exactly the number the board asks for — one on the small board, two on the others.

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.

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 row’s star too. Everything else in the row is out. 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; it works with any number, and with columns just the same.

With two stars a line the touching rule does most of the work: a 2 × 2 block can hold one star at most, and so can three cells in a row. A region shaped like a bent stick has room for two stars in only one or two ways.

Sometimes counting runs dry. Then suppose a star in some cell and see what it crosses out — if a region is left with nowhere to put its star, the supposition was wrong and the cell is crossed. One step deep is the whole technique; a supposition that needs a second one is guessing.