I solve LinkedIn Queens #801 row by row on a 9×9 grid. 9 regions, 9 queens total. My final map: R1C4, R2C2, R3C6, R4C9, R5C5, R6C8, R7C3, R8C1, R9C7. 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 R1C4. Row 1, column 4 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 R2C2. Row 2, column 2 is the forced queen once region 2, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 3 at R3C6. Row 3, column 6 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 4 at R4C9. Row 4, column 9 is the forced queen once region 4, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 5 at R5C5. Region 5 only touches row 5 once on this board, so its queen must land at column 5. That clears a chunk of the grid via auto X marks.
I place queen 6 at R6C8. Region 7 only touches row 6 once on this board, so its queen must land at column 8. That clears a chunk of the grid via auto X marks.
I place queen 7 at R7C3. Row 7, column 3 is the forced queen once region 6, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 8 at R8C1. Region 8 only touches row 8 once on this board, so its queen must land at column 1. That clears a chunk of the grid via auto X marks.
I place queen 9 at R9C7. After eliminations, row 9 has one legal square left — column 7. That clears a chunk of the grid via auto X marks.
Done — R1C4, R2C2, R3C6, R4C9, R5C5, R6C8, R7C3, R8C1, R9C7. 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.