How to solve a queens puzzle, step by step

The few techniques that solve most queens puzzles: marking around a queen, regions stuck in one row, pairs of regions, and cells that would empty a region.

A queens puzzle has one rule set: one queen in every row, every column and every coloured region, and no two queens touching, not even corner to corner. You never need to guess. Each step below finds a queen, or a cell that can’t hold one, from what’s already on the board.

A solved 5×5 queens puzzle. One crown in each row, column and region, and none of them touch.

Mark around every queen

A queen takes a lot of the board with it. Its row, its column and its region can’t hold another queen, and neither can the eight cells around it. Mark all of them with a dot as soon as you place a queen. Dots are notes: they only say “no queen here”.

One queen rules out its row, its column, its region and the eight cells around it.

Most of the puzzle is this step on repeat. After each queen, look at what the new dots leave behind: a region or a line with only one empty cell left gets its queen there.

Start with the small regions

A region of one cell is a queen straight away. A region of two or three cells has few places to go, and its queen will usually rule out a lot of the board once you find it. Small regions are the first place to look on a new puzzle.

A region that sits in one row

If a whole region lies inside one row, that row’s queen has to be in that region. So every other cell of the row is out, even in other regions. The same works for a region that sits inside one column.

The highlighted region lies in one row. Its queen is that row's queen, so the other two cells in the row get dots.

Two regions in two rows

The same idea works with more regions. If two regions fit inside the same two rows, those two rows’ queens are in those two regions. Every other cell of those two rows is out. Three regions in three rows, or three in three columns, work the same way.

Two regions fit inside the first two columns, so those columns' queens are theirs. The rest of the two columns gets dots.

This step is easy to miss, because the rows look busy. Look for regions that stay within a narrow band of the board.

Cells that would empty a region

Before you place a queen, check what it would rule out. If a queen on a cell would take every empty cell of some other region, that region would have nowhere left for its queen. So the cell can’t hold a queen.

A queen on either dotted cell would touch both cells of the small region next to it, leaving it empty. Neither cell can hold a queen.

This mostly helps next to small regions, and along the edge of a row or column with only two or three empty cells left.

Putting it together

Mark around every queen you place.
Fill any region, row or column that has one empty cell left.
Look for regions that sit inside one row or column, then pairs of regions in two rows or columns.
Check the cells next to small regions for ones that would empty them.

Then go back to step 1. On most boards you’ll only need the first three. Harder boards need the last one a few times.

Two-star puzzles work the same way with two queens, or stars, per row, column and region. They’re called star battle.