Two regions, two rows
Suppose regions A and B can place their crowns only in rows 2 and 4. They need two crowns in different rows, and only those two rows are available. Both rows are reserved for A and B, so candidates from every other region in rows 2 and 4 can be crossed out.
The same counting proof works for columns and for three regions confined to three lines. Count the union of every candidate line in the selected regions. If a third row is still available to a pair, the two-row reservation has not been proved.
- Start with two regions that each have few candidate rows or columns.
- The number of different available lines must equal the number of regions.
- A set with fewer lines than regions indicates a contradiction in the position.
- Do not choose which of the two regions uses which row yet. First remove outside candidates.
Why it works
Two regions need two crowns in two different rows. If both regions fit entirely inside the same two rows, those two rows must hold exactly these two crowns. No other region can use either row, so their cells there are eliminated. With three regions in three rows (or columns) the same counting works.
This group lock is the signature technique of hard Queens puzzles. It appears more often as boards grow, and it carries the most weight in our difficulty rating.
How to spot it fast
- Look for two small or narrow regions stacked in the same pair of rows or columns.
- Count lines, not cells: the regions may cover several cells, but they must use only two rows between them.
- After eliminating, check the trimmed regions — group locks usually unlock a forced crown elsewhere.
Common mistakes
- Counting a third row that one region can still reach. Then there is no reservation.
- Deciding which region takes which row. The lock only clears the outside cells; the order comes later.
Try one move
Tap a still-open cell this deduction rules out. This is a real position from 5×5 puzzle #5-standard-002.
👑 placed crown · × already ruled out · · still a candidate. Row and column numbers start at 1.
A real example from the game
This position comes from 7×7 puzzle #5, after 2 earlier deductions. The highlighted cells show where the technique applies.
A set of regions reserves these columns
Regions A, D, E can only fit on columns 1, 2, 3 — exactly as many regions as columns. Those columns are fully reserved, so every other candidate on them is ruled out.
Play this board and look for the same move yourself.
How often this technique appears
Across all 4,000 levels, our logic engine needs this technique on the following share of boards at each size:
| Board size | Boards that need it |
|---|---|
| 5×5 | 17% |
| 6×6 | 43% |
| 7×7 | 45% |
| 8×8 | 56% |
| 9×9 | 58% |
| 10×10 | 45% |
| 11×11 | 72% |
| 12×12 | 95% |
Questions about this technique
What is the hardest technique in Queens puzzles?
Region groups (two regions confined to the same two rows or columns, or three to three) are the most advanced common technique. They appear in most 11×11 and 12×12 boards and are weighted highest in our difficulty rating.