Queens Puzzle Solver

How to use the Queens puzzle solver

Choose the size of your grid, pick a colour and tap or drag over the squares of one region, then the next colour for the next region, until every square is coloured. The colours do not have to match your puzzle's; only which squares belong together matters. Press Explain the next step and the solver places a queen or crosses out squares, highlights what proves it, and says why. Show the answer places every queen at once and checks there is only one solution.

It solves the colour-region Queens puzzles that appear daily in apps such as LinkedIn's; Greg Puzzles is not affiliated with LinkedIn. The puzzle itself is older: it is a one-star Star Battle.

The rules

Put one queen in every row, every column and every coloured region, so a grid of 8 by 8 with 8 regions gets 8 queens. No two queens may touch, not even corner to corner. Unlike the eight queens puzzle, queens may share a diagonal as long as they are not next to each other.

How to solve Queens puzzles, step by step

Start with the smallest regions. A region of one square is a queen straight away, and placing it crosses out its row, its column and the eight squares around it. A region that lies entirely in one row owns that row's queen: cross out every other square in the row.

Count regions against rows. The same idea grows: if two regions fit entirely within two rows, those two rows' queens are theirs, and nothing else in those rows can have one. The same goes for columns.

Ask what a queen would leave. When nothing simple is left, take a square and imagine a queen on it. If that would cross out every open square of some region, row or column, the square cannot be a queen. Expert players do this in their heads; the solver writes it out.

How it was checked

On 60 random colourings its count of solutions matched a brute-force search through every way to put one queen in each row. It was then run on puzzles from 5 by 5 to 11 by 11, made by placing queens at random and growing a region round each, kept only when they had a single solution: it found every answer, never placed a queen wrongly or crossed out a square that held one, and explained every puzzle from start to finish.

More queens

The classic version, with no colours and queens attacking along diagonals too, is the eight queens puzzle, with all 92 solutions and the search shown step by step. Our chess puzzles Queen's Attack and Swapping Castles are played with real pieces and ordinary chess moves. There are more solvers on the puzzle tools page.