How to solve Queens puzzles

Queens puzzles (also called Star Battle) became a daily habit for millions of people. The rules are short: a square grid is split into coloured regions; place exactly one queen in every row, every column and every region, and no two queens may touch, not even diagonally. In ChikiDoku the queens are chicks and the regions are nests, but the logic is exactly the same.

A well-made Queens puzzle has exactly one solution and never needs a guess. You solve it by ruling squares out until only one place is left for a piece. These are the techniques, from the easiest to the hardest, in the order ChikiDoku's own hints (Mama Hen) use them.

• 1One chick in every row and every column
• 2One chick in every coloured nest
• 3Chicks never touch, not even at the corners

1. Mark what can't be

Before anything else, learn to mark. When you are sure a square cannot hold a queen, put a mark on it (in ChikiDoku, tap once to lay an egg). Most of solving is marking: a piece is placed only when every other square of a row, column or region has been ruled out. Every time you place a piece, mark its whole row, its whole column, its whole region and the eight squares around it.

2. The one-square region

If a region is a single square, its queen must be there. Place it, then mark everything it rules out. Larger regions that are a straight line of two or three squares are almost as good: whichever square holds the queen, some squares around them are always ruled out. Mark those.

3. The last place in a line

Look along each row and each column. If only one unmarked square is left in a line, the line's queen goes there. Do the same for each region: a region with one free square left has found its queen.

4. A region trapped in one line

If every free square of a region lies in the same row, that row's queen must belong to this region. So every other square of that row, outside the region, can be marked. The same works for columns. This is the move that cracks most medium puzzles.

5. Squares that touch everything

Sometimes a square touches every free square of a region (it sits next to all of them, including diagonally). A queen on that square would leave the region with nowhere to go, so mark it. The same idea works with a whole row or column: if a square touches every free square of a line, it is out.

6. Two regions, two lines

If two regions together fit only inside the same two rows, those two rows are used up by those two regions. Every other square of the two rows can be marked. It works with three regions in three rows, and with columns. Expert puzzles are built on this idea, and spotting it feels wonderful.

Tips that save time

• Start with the smallest regions and the regions squeezed against an edge.
• After every placement, do all the marking it allows before looking for the next move.
• When stuck, count: N regions must fill N rows. Look for a group of regions that fits in the same number of lines.
• Never guess. If you need to guess, a mark is missing somewhere. Go back over each region with technique 4.