A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on, till the topmost floor is numbered 6. B lives on a floor that is a prime number. The product of floors on which B and D live is 3. Only 2 people live above C. F lives immediately below A. How many people live between A and C?
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Solving the Building Floors Logic Puzzle
This puzzle requires careful deduction based on the given clues about six people (A, B, C, D, E, F) living on six floors of a building, numbered 1 to 6 from bottom to top.
Step-by-Step Deduction:
- Clue 1: Floors are numbered 1 to 6. The lowest floor is 1, and the topmost is 6.
- Clue 2: B lives on a prime-numbered floor. The prime numbers between 1 and 6 are 2, 3, and 5. So, B lives on floor 2, 3, or 5.
- Clue 3: The product of floors on which B and D live is 3. This can be written mathematically as
B_{floor} \times D_{floor} = 3. Since floors are integers, the only possible pairs of floors for (B, D) are (1, 3) or (3, 1). - Combining Clue 2 and Clue 3: We know B's floor must be prime.
- If (B, D) = (1, 3), then B is on floor 1. Floor 1 is not prime. This combination is invalid.
- If (B, D) = (3, 1), then B is on floor 3. Floor 3 is prime. This combination is valid.
- Clue 4: Only 2 people live above C. If 2 people live above C, C must be on the floor such that there are exactly two floors higher than C's floor. In a 6-floor building, this means C lives on floor 4 (floors 5 and 6 are above floor 4). So, C lives on floor 4.
- Clue 5: F lives immediately below A. This means A's floor number is one greater than F's floor number. Possible pairs (F, A) are (1, 2), (2, 3), (3, 4), (4, 5), or (5, 6).
Determining F and A's Floors:
Let's check the possible pairs for (F, A) against the floors already occupied:
- D is on floor 1.
- B is on floor 3.
- C is on floor 4.
Now, let's examine the possible (F, A) pairs:
- (1, 2): Invalid, D lives on floor 1.
- (2, 3): Invalid, B lives on floor 3.
- (3, 4): Invalid, C lives on floor 4.
- (4, 5): Invalid, C lives on floor 4. F cannot be on the same floor as C.
- (5, 6): This pair is valid as floors 5 and 6 are currently unoccupied.
Therefore, F lives on floor 5 and A lives on floor 6.
Final Arrangement and Answer:
The final arrangement of people on the floors is:
| Floor 6: A |
| Floor 5: F |
| Floor 4: C |
| Floor 3: B |
| Floor 2: E (The only remaining person and floor) |
| Floor 1: D |
The question asks: How many people live between A and C?
- A lives on floor 6.
- C lives on floor 4.
- The floor between them is floor 5.
- F lives on floor 5.
Therefore, there is 1 person (F) living between A and C.
Important Questions from Floor Puzzle
- If P is on the first step, on which step is S?
- If P is on the first step, which of the following is true?
- If T was on the third step, which of the following pairs is incorrect?
If T joined P, Q, R and S, and T was on the third step, and Q was on a higher step than T, which step must be vacant?
If there are two steps in between the steps on which A and D are standing and C is standing on Step 6, A must be standing on which of the following steps?
