The four rules
- Place one queen in every row.
- Place one queen in every column.
- Place one queen in every coloured region.
- Queens cannot touch, even diagonally.
Start with regions that have very few options
Scan each coloured region before placing anything. If a region can only use one square because the other squares clash with a row, column or neighbouring queen, that placement is forced. These forced moves are more reliable than guessing at an open area.
Use the non-touching rule aggressively
When you place a queen, cross out the eight squares around it immediately. It is easy to remember the row and column rule while missing a diagonal neighbour. On a crowded board, that small exclusion is often what leaves a nearby region with one legal square.
Check rows and columns after every placement
A row or column with a queen is complete. A row or column with only one remaining candidate is also complete, even if you found the answer through a different region. Move between regions and lines rather than trying to solve one area in isolation.
When you are stuck
Do a clean pass: count candidates in every region, then every row, then every column. Do not guess because two squares look equally likely. A forced move is usually waiting in a different part of the board.