Single-cell region
Essential 66% of boards
This colour covers only one cell, so its queen goes there.
A real 6×6 board after no moves . From here a queen must go at A3.
Queens Solving Techniques
These are the deductions the hint button uses, in the order worth learning them. Each is shown on a real position from a real board in the catalogue, and the frequency figures come from running the engine over all 15,333 puzzles.
How often you need each one
| Technique | Boards that need it |
|---|---|
| Single-cell region | 66% |
| Forced queen | 100% |
| Last cell in a line | 55% |
| Region line lock | 93% |
| Line uses one region | 41% |
| Shared diagonal neighbour | 75% |
| Two-region group lock | 36% |
| Multi-region group lock | 14% |
| Lines use the same regions | 7% |
| Split-line region lock | 13% |
| Split-line colour lock | 2% |
| Ruled out either way | 30% |
| Test a queen | 9% |
A deduction can often be reached more than one way, so read these as how often the engine reached for each, not as a unique decomposition.
Essential techniques
Every board uses these. Learn them first.
Forced queen
Essential 100% of boards
This colour has one legal cell left, so its queen goes there.
A real 6×6 board after 7 deductions . From here a queen must go at E2.
Last cell in a line
Essential 55% of boards
Column 2 has one legal cell left, so its queen goes there.
A real 6×6 board after 6 deductions , with 2 queens placed . From here a queen must go at B6.
Region line lock
Essential 93% of boards
This colour must use column 5, so nothing else can.
A real 6×6 board after no moves . From here E3, E4, E5, E6 can be ruled out.
Intermediate techniques
The workhorses. Most boards need at least one.
Line uses one region
Intermediate 41% of boards
1 rows can only be filled by 1 colours, using them up.
A real 6×6 board after 1 deductions . From here D5, F5 can be ruled out.
Shared diagonal neighbour
Intermediate 75% of boards
Every remaining option for this colour touches these cells, so they are out.
A real 6×6 board after 2 deductions . From here D1, F1, D2, F2 can be ruled out.
Two-region group lock
Intermediate 36% of boards
2 colours fit in only 2 rows, reserving them.
A real 6×6 board after 3 deductions . From here C1, D1, C2 can be ruled out.
Multi-region group lock
Intermediate 14% of boards
3 colours fit in only 3 columns, reserving them.
A real 6×6 board after 3 deductions . From here C4, C5 can be ruled out.
Lines use the same regions
Intermediate 7% of boards
2 rows can only be filled by 2 colours, using them up.
A real 6×6 board after 4 deductions . From here F3, F4 can be ruled out.
Split-line region lock
Intermediate 13% of boards
2 colours fit in only 2 columns, reserving them.
A real 11×11 board after 5 deductions , with 5 queens placed . From here C6, C11 can be ruled out.
Split-line colour lock
Intermediate 2% of boards
2 rows can only be filled by 2 colours, using them up.
A real 11×11 board after 9 deductions , with 5 queens placed . From here D3, K3, D4, K4 and 3 more can be ruled out.
Expert techniques
For boards where nothing else moves.
Ruled out either way
Expert 30% of boards
These cells are ruled out no matter where this colour's queen goes.
A real 6×6 board after 3 deductions , with 2 queens placed . From here F4 can be ruled out.
Test a queen
Expert 9% of boards
A queen here would leave another colour with nowhere to go, so it is out.
A real 6×6 board after 7 deductions , with 2 queens placed . From here C4 can be ruled out.
Why you never have to guess
Every board in the catalogue has exactly one solution, verified by exhaustive search, and every one can be finished using only the techniques above — checked by solving all 15,333 with this engine. If a board stops moving, the deduction you need is on this page.
Ready to apply them? Start with the daily puzzle, or pick a size and difficulty.