Queens Max

How to solve Queens puzzles

Ten techniques, ordered by how much work they take to spot. The hint button in the game names whichever one applies to your board and links back here — so if a hint ever confuses you, the explanation is one click away.

Start here

Counting. These three finish most boards on their own.

  1. Adjacency elimination

    The first move after every placement — a queen clears her row, her column, her colour, and all eight squares she touches.

  2. Region completion

    When a colour has one square left, the queen goes there. The simplest deduction in the game and the one that unlocks everything else.

  3. Container completion

    Rows and columns need queens too. One uncrossed square left in a line means the queen goes there.

Reasoning about sets

Conclusions drawn without knowing where a queen goes.

  1. Region containment

    A colour trapped inside one row or column owns that line — every other colour has to leave it.

  2. Row and column confinement

    When a whole row can only be served by one colour, that colour is used up here — and disappears from the rest of the board.

  3. Locked queen placement

    Squares attacked by every remaining option are dead — even before you know which option is right.

Hard boards

Pigeonhole counting, geometry, and one honest hypothetical.

  1. Simple undercounting

    Two colours that fit in only two rows fill those rows completely. Pigeonhole logic, and the first truly hard technique.

  2. The rule of crowding

    Count in the other direction — when three rows can only be served by three colours, those colours belong to those rows and nowhere else.

  3. The rule of clumps

    Queens in touching rows need two columns of clearance. When one option would swallow the whole row next door, it is not an option.

  4. Exclusion logic

    The last resort, and still not guessing — try a square, push the easy logic two steps, and rule it out when the board breaks.