Learn how to use region size and shape to narrow down queen placements in Queens puzzles.

What Is Region Elimination?

Region elimination is the most fundamental Queens solving technique. The idea is simple: since each colored region must contain exactly one queen, you can use the size and shape of regions to determine where queens must go. A region with only one cell gives you a free queen placement. A region with two or three cells severely limits your options.

How to Apply It

Start every puzzle by scanning for the smallest regions. Count the cells in each region and rank them from smallest to largest. Begin placing queens in the most constrained regions. After each placement, eliminate the queen's row, column, and adjacent cells from other regions. This often reduces other regions to just one or two valid cells, creating a cascade of forced placements.

When a Region Spans One Row or Column

Pay special attention to regions whose cells all fall in a single row or column. If region A occupies only cells in row 3, then row 3's queen must belong to region A. No other region can place a queen in row 3. This is a powerful deduction that can unlock the rest of the puzzle.

Common Mistakes

Don't forget the adjacency constraint when evaluating regions. A region might have three cells, but if two of them are adjacent to an already-placed queen, only one cell remains valid. Always check adjacency after row/column elimination.

Practice Tips

Start with 5x5 and 6x6 puzzles where region elimination alone can solve most of the grid. As you move to larger grids, you'll combine region elimination with other techniques like row-column scanning and intersection analysis.