Queens Solving Techniques

The eight deductions that crack every board — the same ones our hint system uses, in the order it tries them.

The guide in five bullets

How to solve step by step

Run this four-pass loop from the top every time you get stuck — it is the same order the hint engine scans.

  1. Pass 1 — Forced queens and direct elimination. Scan every row, column, and region for a single remaining candidate and place that queen. After each placement, X out its row, column, region, and diagonal neighbors (Forced Queen, Row/Column Elimination).
  2. Pass 2 — Line locks. Look for a region confined to one row or column — that line's queen must be inside it, so X the rest of the line everywhere else (Region Line Lock). Repeat Pass 1 after every lock; a lock usually creates new forced queens.
  3. Pass 3 — Group counting. When line locks run out, look for k regions confined to k lines (or k lines drawing only from k regions) and X out the crossover cells (Region Group Lock, Line Group Lock). This is the most powerful technique on 9×9 and larger boards.
  4. Pass 4 — Test and follow. If the board is still not solved, test a candidate queen and follow the forced Xs it creates (Diagonal Neighbor Elimination, Test a Queen, Follow a Test Chain). A contradiction proves the candidate impossible; eliminate it and return to Pass 1.

Essential techniques

Forced Queen

How to spot it
A row, column, or region that has exactly one cell still open (every other cell is X'd out).
What to do
Place a queen in that single open cell — it is the only place the line or region can hold its queen.
Why it works
Every row, column, and region needs exactly one queen. If only one candidate cell remains, that cell must be the queen; there is no other option.
When it applies
Constantly, and especially near the end of a solve. Any time you finish X'ing out a line or region, check whether it now has a single survivor.

Row / Column Elimination

How to spot it
A queen you have already placed sharing a row or column with open cells.
What to do
X out every other cell in that queen's row and column, plus its four diagonal neighbors.
Why it works
Only one queen may sit in each row and each column, and no two queens may touch. So the rest of the row, the rest of the column, and the diagonal neighbors can never hold a queen.
When it applies
Immediately after every queen you place. Auto-X does this for you, but understanding it lets you read the board without the crutch.

Region Line Lock

How to spot it
A colored region whose open cells all lie within a single row or a single column.
What to do
X out that whole row (or column) everywhere it leaves the region — no other region can take the line's queen.
Why it works
The region needs a queen, and its only candidates are in this one line. So the line's single queen must belong to this region, which forbids the line's cells in every other region.
When it applies
Early in a solve. Regions squeezed into one line are the strongest opening moves and start a cascade of eliminations.

Intermediate techniques

Diagonal Neighbor Elimination

How to spot it
Two lines (rows or columns) that must each place a queen in the same pair of adjacent columns (or rows).
What to do
X out the cells where those queens would end up diagonally touching, removing the touching candidate pairs.
Why it works
Queens can never be adjacent, even diagonally. When two forced queens would land in touching cells, that arrangement is illegal, so those specific candidates can be eliminated.
When it applies
In the middle of a solve, when two regions or lines compete for a narrow band of adjacent cells.

Region Group Lock

How to spot it
A group of k colored regions whose combined open cells occupy exactly k rows (or exactly k columns).
What to do
X out every cell of those k rows that belongs to a region outside the group.
Why it works
Those k regions need k queens, and they can only be placed within those k rows. That uses up all the queens those rows can hold, so no outside region may place a queen there.
When it applies
On larger boards (9×9 and up), when a cluster of regions shares a short band of lines. It is the single most powerful counting technique.

Line Group Lock

How to spot it
A group of k rows (or columns) whose queens must all come from the same k colored regions.
What to do
X out those regions' cells everywhere outside the k lines.
Why it works
This is the mirror of the region group lock: if k lines can only draw their queens from k regions, those regions are fully committed to those lines and have nothing left to give elsewhere.
When it applies
Alongside the region group lock; whichever framing is easier to see on the current board.

Expert techniques

Test a Queen

How to spot it
A hard position where no direct elimination is visible, but a region or line has just a few candidates.
What to do
Tentatively assume one candidate is the queen, follow the forced Xs it creates, and see whether it leads to a contradiction (a line or region left with no room for a queen).
Why it works
If assuming a queen in a cell breaks the board, that cell cannot be a queen and can be X'd. Every Queens board has exactly one solution, so a contradiction is proof.
When it applies
Only when the direct techniques stall. It is slower, so save it for genuine dead ends.

Follow a Test Chain

How to spot it
A test-a-queen assumption that forces a long sequence of further placements before resolving.
What to do
Keep following the chain of forced queens and Xs from your assumption until it either solves a large area or hits a contradiction.
Why it works
A single test can ripple through many regions. Following the whole chain either confirms a series of placements or disproves the starting assumption, unlocking the board.
When it applies
The deepest boards (11×11 and 12×12), where the final deductions require reasoning several moves ahead.

Quick tips

Common mistakes

These are the exact eight deductions our in-game hint system uses, described accurately and in the order it tries them — nothing here is simplified or invented. Learn them here, then put them to work on today's daily challenge, an unlimited board, or any puzzle in the numbered library.

New to the game? Start with the how to play guide for the rules and controls, or see how this puzzle style compares to the original on the LinkedIn Queens page.

Practice on today's challenge Back to how to play

Frequently asked questions

Do I need to memorize all eight techniques?

No. Learn the three Essential techniques first — Forced Queen, Row/Column Elimination, and Region Line Lock — and you can already solve most 7×7 and 8×8 boards. Add the Intermediate techniques for 9×9 and 10×10, and the Expert pair only for the hardest 11×11 and 12×12 boards.

What order should I learn the techniques in?

The order on this page: Essential, then Intermediate, then Expert. It matches the four-pass scan loop above and the order the in-game hint engine tries them in, so learning them in order is the fastest way to stop needing hints.

Why does a hint sometimes name a technique I haven't learned yet?

The hint engine always returns the simplest technique that makes progress on the current board. If it names an Intermediate or Expert technique, it means every Essential technique has already been applied — a good sign you are near the end of the easy part of the solve.

Do bigger boards need different techniques?

The same eight techniques apply at every size from 5×5 to 12×12. Larger boards just need them more often and in longer chains — Region Group Lock and Line Group Lock do most of the work on 9×9 and up, and Follow a Test Chain becomes more common on 11×11 and 12×12.

What if I place a queen and it turns out to be wrong?

Every board has exactly one solution, so a wrong queen always creates a contradiction somewhere — a line or region left with no legal candidate. The in-game hint checks for this first and will tell you which queen to remove before offering the next deduction.

Is every Queens board solvable without guessing?

Yes. Because each board has a unique solution, Follow a Test Chain is a guaranteed fallback: testing a candidate and following the forced moves it creates always either confirms a run of placements or hits a contradiction. No board ever requires an actual guess.