How to Solve Queens Puzzles

The rules of Queens

1. One queen in every row.
2. One queen in every column.
3. One queen in every color region.
4. No two queens touch, not even diagonally.

An N×N board therefore has exactly N queens and N regions. Every puzzle on this site, and in our Crowns app, has been checked by a solver to have exactly one solution, so you never need to guess. These are also the rules of LinkedIn’s daily Queens game and of one-star Star Battle puzzles.

Step by step: how to solve any Queens puzzle

1. Learn the four rules. Exactly one queen in every row, every column and every color region, and no two queens touching, not even diagonally.
2. Start with the smallest or most cramped region. A region with two or three cells, or one squeezed into a single row or column, has very few places for its queen.
3. Mark impossible cells with X. Every time you know where a queen can’t go, mark it. Every queen you place rules out its row, its column, its region and the eight cells around it.
4. Look for regions confined to one row or column. If all of a region’s open cells are in one row, that row’s queen belongs to that region. X out the rest of the row. The same works for columns.
5. Count regions against rows and columns. If two regions fit entirely inside the same two rows, those two rows are used up by those regions. X out every other cell in those rows. This works for any number of regions.
6. Use the touching rule to eliminate cells. If a cell touches (or shares a row or column with) every open cell of a region, a queen there would leave that region empty. X it out.
7. Place queens only when forced, and repeat. When a row, column or region has only one open cell left, place the queen there, mark everything it rules out, and go back to step 4.

Worked example (5×5)

Five techniques that solve almost every Queens puzzle

1. Singles

If a row, column or region has only one open cell, the queen goes there. Place it, then X its row, column, region and the eight cells around it.

2. Confinement (a region trapped in a line)

If all of a region’s open cells are in one row, that row’s queen must be in the region. X every other cell in the row. The same applies to columns. This is the most common move in Queens.

3. Counting regions (pigeonhole)

If k regions fit entirely inside the same k rows, those rows are taken. Every other region’s cells in those rows can be X’d. Look for two regions inside two rows and three regions inside three columns. On bigger boards this is how most hard puzzles break open.

4. The touching test

Pick a cell and ask: if a queen went here, would some region lose all of its open cells? A queen rules out its row, column and the eight cells around it. If that covers every open cell of a region, the cell is impossible. It works especially well next to small regions.

5. The 2×2 rule

Any 2×2 block can hold at most one queen, because its four cells all touch each other. Two neighbouring rows therefore hold exactly two queens at least two columns apart, and the same goes for columns. Counting this way often settles the last few cells of a hard puzzle.

Common mistakes

• Placing queens too early. Mark X’s first. Place a queen only when it is forced.
• Forgetting diagonals. Queens can’t touch at the corners either.
• Only looking at regions. Rows and columns create just as many deductions, so scan all three.

Practice

The fastest way to improve is to solve a lot of puzzles. Play the free daily Queens puzzle (it gets harder through the week), switch to unlimited for 5×5 to 12×12 boards, or check today’s hints if you’re stuck.

Play today’s Queens puzzle →

Queens FAQ