LinkedIn Queens #764 Answer & Analysis

The starting board already gives queens at R1C4 and R2C6. Lock those in first, then eliminate their rows, columns, and all touching neighbors. That immediately trims the top-left, top-middle, and upper-right candidate cells.

The green color region is tiny, so once column 4 is blocked by the fixed queen at R1C4, the only surviving green choice is R4C5. That places a queen in the center-right of the board and helps separate the middle rows.

The orange region has to fit into the top half without touching the fixed queen at R2C6. The diagonal from that queen knocks out R3C7, so the far-right safe square becomes the orange queen placement.

With the upper rows constrained, the gray region is pushed into row 5, and the red region must use row 6. Column 8 is already occupied by the orange queen at R3C8, so the red queen cannot go there and must take the other red square in row 6.

The last two regions are the yellow and beige areas. They settle into R7C1 and R8C3, which completes the row, column, and region coverage without any touching queens. At this point the board is fully solved and every constraint checks out.