I solve LinkedIn Queens #806 row by row on a 9×9 grid. 9 regions, 9 queens total. My final map: R1C5, R2C8, R3C2, R4C6, R5C3, R6C9, R7C4, R8C7, R9C1. X marks do most of the work before I commit each crown.
Before placing anything I mark X on every cell blocked by givens — then I hunt the tightest region. Several color regions span only a few cells — scan those regions first because they often force a queen into a single row or column.
I place queen 1 at R1C5. Row 1, column 5 is the forced queen once region 1, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 2 at R2C8. Row 2, column 8 is the forced queen once region 3, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 3 at R3C2. Region 2 only touches row 3 once on this board, so its queen must land at column 2. That clears a chunk of the grid via auto X marks.
I place queen 4 at R4C6. Row 4, column 6 is the forced queen once region 5, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 5 at R5C3. Column 3 is the only column still available for a queen in row 5. That clears a chunk of the grid via auto X marks.
I place queen 6 at R6C9. Region 6 only touches row 6 once on this board, so its queen must land at column 9. That clears a chunk of the grid via auto X marks.
I place queen 7 at R7C4. Region 8 only touches row 7 once on this board, so its queen must land at column 4. That clears a chunk of the grid via auto X marks.
I place queen 8 at R8C7. Region 9 only touches row 8 once on this board, so its queen must land at column 7. That clears a chunk of the grid via auto X marks.
I place queen 9 at R9C1. After eliminations, row 9 has one legal square left — column 1. That clears a chunk of the grid via auto X marks.
Done — R1C5, R2C8, R3C2, R4C6, R5C3, R6C9, R7C4, R8C7, R9C1. Every row and region checked twice. Several color regions span only a few cells — scan those regions first because they often force a queen into a single row or column.