In a building with three floors, floor 2 is above floor 1, and floor 3 is above floor 2. Each floor has two flats: Flat A is to the west of Flat B. Ea...

In a building with three floors, floor 2 is above floor 1, and floor 3 is above floor 2. Each floor has two flats: Flat A is to the west of Flat B. Each flat has an area of 576 ft² and a distinct number of rooms. The area of each room in one of the flats on an even-numbered floor is 64 ft². The total number of rooms on the third floor is 7. The flat with rooms of area 72 ft² is on an odd-numbered floor. The flat directly below the flat with 9 rooms has rooms of area 288 ft². There is exactly one floor between the flat with room area 192 ft² and the flat with room area 72 ft². There is no flat to the west of the flat having 6 rooms.

Question: How many rooms are there in the flat to the west of the flat whose each room area is 288 ft²?