Step 1: The Orange region sits entirely in row 3, so no other queen can go in row 3. The Blue region sits entirely in row 5, so no other queen can go in row 5. The Pink region sits entirely in row 2, so no other queen can go in row 2. The Purple, Orange and Blue regions sit entirely in columns 1, 2 and 3, so no other queen can go in those columns. The Purple, Green, Yellow, Red and Gray regions sit entirely in rows 4, 6, 7, 8 and 9, so no other queen can go in those rows. A queen in row 1, column 6 would leave the Pink region with no open square, so that square is out. A queen in row 1, column 7 would leave the Pink region with no open square, so that square is out. A queen in row 4, column 1 would leave the Orange region with no open square, so that square is out. A queen in row 4, column 2 would leave the Orange region with no open square, so that square is out. A queen in row 4, column 3 would leave the Blue region with no open square, so that square is out. The Purple region sits entirely in row 6, so no other queen can go in row 6. A queen in row 5, column 2 would leave the Purple region with no open square, so that square is out. The Blue region has only one open square left, so its queen goes in row 5, column 3 (R5C3).