I solve LinkedIn Queens #816 row by row on a 9×9 grid. 9 regions, 9 queens total. My final map: R1C5, R2C2, R3C4, R4C7, R5C3, R6C8, R7C1, R8C9, R9C6. 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 2, 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 1, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 3 at R3C4. Row 3, column 4 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 4 at R4C7. Region 5 only touches row 4 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 5 at R5C3. Row 5, 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 6 at R6C8. Region 3 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 R7C1. Region 9 only touches row 7 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 8 at R8C9. After eliminations, row 8 has one legal square left — column 9. That clears a chunk of the grid via auto X marks.
I place queen 9 at R9C6. After eliminations, row 9 has one legal square left — column 6. That clears a chunk of the grid via auto X marks.
Done — R1C5, R2C2, R3C4, R4C7, R5C3, R6C8, R7C1, R8C9, R9C6. 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.