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?

Question

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?

Accepted Answer

**Solution:**

1. Each flat has an area of 576 ft².

2. The number of rooms in a flat = Total flat area ÷ Area of each room.

3. The flat with room area 288 ft² has number of rooms = $ \frac{576}{288} = 2 $ rooms.

4. The flat directly below the flat with 9 rooms has rooms of area 288 ft², so the flat with 9 rooms is on floor 2 or 3, and the flat with 2 rooms is directly below it.

5. The flat with rooms of area 72 ft² is on an odd-numbered floor.

6. Total rooms on floor 3 are 7.

7. There is one floor between the flat with room area 192 ft² and the flat with room area 72 ft².

8. No flat is to the west of the flat having 6 rooms, so the flat with 6 rooms must be on the west side.

9. Using these clues and the fact that Flat A is always west of Flat B, we deduce that the flat to the west of the flat with room area 288 ft² has 6 rooms.

**Answer:** 6

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