Stars strategy: ruling cells out

In Stars you rarely find a star directly. You find all the places it can't be, until there's only one place left. Every technique below is a way of crossing cells out.

How the difficulty works

Each tier is set by the hardest step you'll need:

• Easy (6×6, one star each) needs only the basics: around a star, full lines and regions, the last open cell, and cells that would starve a region.
• Medium (8×8, one star each) needs at least one region confined to a single row or column.
• Hard (10×10, two stars each) needs a group of regions confined to the same number of lines, or a short what-if.

The basics

Three moves happen all the time, and soon become automatic:

• Around a star: the cells touching it, diagonals included, are empty.
• Full: a row, column or region with all its stars has no room for more, so the rest of it is empty.
• Last cells: a row, column or region with exactly as many open cells as stars still needed — they're all stars.

A star that would starve a region

The fourth basic move is the one that does the real work. Look at a small region, and at the cells just outside it. If a star in some cell would touch every open cell of that region, the region would be left with nowhere for its star. So that cell is empty.

The same works for rows and columns: a cell whose star would rule out all the remaining cells of some line can't hold a star. On Hard, with two stars each, it extends naturally: a star there would leave a region without room for two non-touching stars.

Medium: a region confined to a line

Sometimes all the open cells of a region lie in a single row (or column). The region's star must be in that row — so the row gets its star from the region, and every other cell in the row is empty. It works the other way round, too: if a row's open cells all lie inside one region, that region's star is in the row, and the rest of the region is empty.

Hard: groups and the what-if

Groups of regions

The confinement idea scales up. If two regions between them only have open cells in two rows, then those two rows get all their stars from those two regions — and every other cell in the two rows is empty. With two stars per region on Hard, count stars rather than regions: two regions needing four stars, inside two rows needing four stars, settle each other.

The what-if

When nothing else works, pick a cell and ask what would happen if it held a star. Cross out its neighbours, fill in whatever follows directly, and see whether some row, column or region runs out of room. If it does, the cell is empty.

Good candidates for a what-if are cells next to small regions or crowded corners, where a star would cross out a lot at once. If a trial doesn't break within a few steps, undo it — our puzzles never need a long one.

Two-star tricks

• Squares of four. Any 2×2 square holds at most one star, since all four of its cells touch each other. So on Hard, a region that fits inside two 2×2 squares has exactly one star in each.
• Three in a row. If a line needs two stars and only has three open cells side by side, the stars are on the ends and the middle is empty.
• The middle of a 2×3. In a region shaped like a 2×3 block, a star in either middle cell would touch all the others, so its two stars sit in the end columns and the middle column is empty.

Good habits

• Start small. The smallest regions and the most crowded lines settle first.
• Dot freely. Dots are free and undoable; a board full of dots makes the remaining choices obvious. Drag to dot a whole row at once.
• After every star, sweep. Its row, column, region and neighbours all change at once.
• Stuck? Hint names the technique and outlines the cells it settles.