I solve LinkedIn Queens #791 row by row on a 8×8 grid. 8 regions, 8 queens total. My final map: R1C6, R2C2, R3C8, R4C5, R5C3, R6C1, R7C7, R8C4. 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 R1C6. Row 1, column 6 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 R3C8. Region 5 only touches row 3 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 4 at R4C5. Row 4, column 5 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 5 at R5C3. Region 6 only touches row 5 once on this board, so its queen must land at column 3. That clears a chunk of the grid via auto X marks.
I place queen 6 at R6C1. Region 7 only touches row 6 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 7 at R7C7. After eliminations, row 7 has one legal square left — column 7. That clears a chunk of the grid via auto X marks.
I place queen 8 at R8C4. After eliminations, row 8 has one legal square left — column 4. That clears a chunk of the grid via auto X marks.
Done — R1C6, R2C2, R3C8, R4C5, R5C3, R6C1, R7C7, R8C4. 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.