Foundation
Eight mistakes that stall a solve
Most lost time in Queens comes from a short list of habits rather than from the difficulty of the boards. Here they are, roughly in order of how much they cost.
1. Skipping the diagonal marks
The largest single source of stalled boards. A queen eliminates the four squares diagonally touching it, and those four are the ones the row-and-column sweep does not cover. Miss one and a forced placement stays hidden indefinitely, with nothing in the resulting position to indicate why. If a board feels harder than it should, audit for this before anything else.
2. Placing a plausible queen
A placement you cannot justify is a guess, whatever it looks like. Every board on this site has exactly one solution reachable by deduction, which means a plausible-looking queen is either redundant — you could have proved it — or wrong. Wrong ones do not announce themselves for several moves, and unwinding them costs far more than the deduction would have.
The test is verbal: say the rule out loud. "This colour has one square left." "This column has one square left." "These two colours take these two rows." If no such sentence is available, the eliminating is not finished.
3. Running only one sweep
The region sweep and the line sweep surface different information at different moments. Colours collapse early because they are small and irregularly shaped; lines collapse late once queens have fragmented the grid. Players who check only colours stall in the endgame; players who check only lines stall in the opening. Alternate deliberately.
4. Over-eliminating on diagonals
The opposite error, and common among players arriving from the classical eight-queens problem. In Queens, the diagonal restriction reaches exactly one square, not the full length of the diagonal. A queen on row 3, column 3 forbids row 4, column 4 — and has nothing to say about row 5, column 5. Eliminating whole diagonals will make a perfectly good board appear unsolvable.
5. Scanning in a fixed pattern
Always starting from the top-left corner wastes most of a sweep. Information in Queens is local and uneven: the squares that changed are the ones near your last placement, and everywhere else is exactly as you left it. Let the last move decide where to look next. On a 12x12 board this one change of habit is worth minutes.
6. Attacking the largest region first
Its shape is often the most eye-catching thing on the board, and it is the least constrained thing on the board. One queen per colour regardless of size means a fourteen-square colour has fourteen candidates and tells you almost nothing. Start with the smallest, and with anything confined to a single row or column.
7. Leaving a hypothetical branch on the board
Testing a candidate by contradiction is a sound technique, but the eliminations a hypothetical queen produces have to come off the board when the test ends. Marks left over from an abandoned branch generate deductions that look valid and are not, and the resulting errors are unusually hard to diagnose because each individual step appears justified.
8. Rushing the last three queens
By the endgame the board is mostly crossed out and the remaining placements look obvious, which is exactly when the no-touching rule gets forgotten. Two of the final queens sitting corner to corner is the standard way to finish a board that will not validate. Check each of the last few against all four constraints before placing it.
Related techniques
- The no-touching rule — The adjacency rule is what makes Queens more than a Latin square, and the diagonal half of it is the most frequently forgotten detail in the game. How to mark it reliably.
- Proof by contradiction — How to test a candidate square in Queens without turning the solve into guesswork: place it hypothetically, follow the forced consequences, and eliminate it when something is stranded.
- The region sweep — The region sweep is the cheapest deduction in Queens and the one most players under-use. How to run it, when to run it, and why it finds queens the line sweep misses.