I solve LinkedIn Queens #821 row by row on a 9×9 grid. 9 regions, 9 queens total. My final map: R1C1, R2C8, R3C6, R4C3, R5C5, R6C7, R7C2, R8C9, R9C4. 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 R1C1. Region 1 only touches row 1 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 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 R3C6. Row 3, 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 4 at R4C3. Row 4, column 3 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. Row 5, column 5 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 R6C7. Row 6, column 7 is the forced queen once region 7, row, column, and touch rules are applied together. That clears a chunk of the grid via auto X marks.
I place queen 7 at R7C2. Row 7, 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 8 at R8C9. Column 9 is the only column still available for a queen in row 8. That clears a chunk of the grid via auto X marks.
I place queen 9 at R9C4. After eliminations, row 9 has one legal square left — column 4. That clears a chunk of the grid via auto X marks.
Done — R1C1, R2C8, R3C6, R4C3, R5C5, R6C7, R7C2, R8C9, R9C4. 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.