How to Solve Queens Puzzles
The rules are simple: one queen per row, column, and coloured region, with no two queens touching. Mastering the techniques takes practice. Here's what actually helps.
Quick rules recap
You have an NxN grid divided into N coloured regions. Place exactly one queen in each row, each column, and each region. No two queens can touch — not even diagonally. Every puzzle has exactly one solution.
Start with small regions
Regions with fewer valid cells are easier to solve. If a region only has cells in one row, the queen must go there. If a region has cells in just two rows, one of those rows must contain the queen. Process the most constrained regions first.
Use elimination
Mark cells that can't contain a queen. If a row already has a queen, mark every other cell in that row. If a column is taken, mark the column. Once a queen is placed, mark all eight adjacent cells. The marks cascade — and suddenly regions have only one valid cell left.
The adjacency constraint is powerful
When you place a queen, all eight surrounding cells are eliminated. This often eliminates cells in neighbouring regions, which forces their queens into specific positions. One placement can cascade across the grid. Work through these implications every time.
Look for forced placements
After elimination, check each row, column, and region. If only one cell remains valid in any of these, the queen must go there. This is the core solving loop: eliminate, find forced placements, repeat.
When stuck, try hypotheticals
If no forced placements remain, pick a cell with few options and ask: if a queen goes here, what follows? If it leads to a contradiction (a row, column, or region with no valid cells), that cell can be eliminated. This technique breaks through harder puzzles.
Practice makes it click
reina has over 340 puzzles across five difficulties. Start with beginner 5x5 grids to build your intuition, then work up to expert 9x9.
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