Step 1: The Red region sits entirely in column 1, so no other queen can go in column 1. The Purple, Orange, Blue, Green, Yellow, Red, Pink and Teal regions sit entirely in rows 2, 3, 4, 5, 6, 7, 8 and 9, so no other queen can go in those rows. A queen in row 4, column 2 would leave the Red region with no open square, so that square is out. A queen in row 5, column 2 would leave the Red region with no open square, so that square is out. A queen in row 6, column 3 would leave the Pink region with no open square, so that square is out. The Purple region sits entirely in column 2, so no other queen can go in column 2. The Yellow region sits entirely in row 9, so no other queen can go in row 9. The Orange, Green, Yellow and Pink regions sit entirely in columns 3, 4, 5 and 6, so no other queen can go in those columns. The Teal region sits entirely in column 7, so no other queen can go in column 7. A queen in row 3, column 2 would leave row 2 with no open square, so that square is out. A queen in row 3, column 3 would leave row 2 with no open square, so that square is out. Row 3 has only one open square left, so its queen goes in column 5 (Orange region) (R3C5).