Queens Rules
Queens puzzles (the one-star form of Star Battle, popularized as LinkedIn Queens) are played on an n×n grid divided into n color regions of irregular connected shapes. You must place exactly n queens so that four rules hold at once: one queen per row, one queen per column, one queen per color region, and no two queens touching, where touching includes all eight directions, diagonals included.
This is a Star Battle at heart. The regions are the puzzle: because each color may only contribute one queen, a color squeezed into two rows tells you immediately that its queen lives there, which eliminates that row for every other color. Solving is a conversation between two counting systems, the rows and columns on one side and the colors on the other, and every elimination in one system echoes through the other.
The method is reservation and elimination: when a line (row or column) or a color has only one cell left that can hold its queen, that cell is forced. When a set of k lines can only be served by k specific colors, those lines belong to those colors exclusively. Every board on this site is machine-verified to be completable by exactly this kind of reasoning, with no guessing at any step.
Step-by-Step: Solving a Queens
- Scan the colors for tight ones. A color confined to a single row (or column) immediately claims that line’s queen.
- Mark eliminations as crosses. Every placed queen crosses out its row, column, color and all eight neighboring cells.
- Hunt for pairs and triples of colors trapped in the same small set of lines; matching counts (two colors, two lines) reserve those lines completely.
- After every placement, re-scan lines and colors with exactly one open cell; those cells are forced queens.
- Repeat until every line and color is satisfied. The finished board has one queen per row, column and color, none of them touching.
Queens Tips & Techniques
- Count colors before rows. If every remaining cell of a color sits inside one row, that row’s queen must be that color, and the color can be crossed out everywhere else.
- Watch for color pairs. When two colors can only live in two particular rows, those rows are spoken for; every other color’s cells in those two rows can be crossed out.
- Use the no-touch rule aggressively. A queen knocks out its eight neighboring cells immediately, so a queen near the middle claims far more territory than an edge queen.
- Think in reservations. A row with a queen is done: cross out all of its remaining cells, then re-check every color that appeared there.
- Never place a queen to "try it out". Every board here is forced step by step; if no line or color argument moves you forward, look at the intersections you have not re-checked yet.
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