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
Seven employees, T, U, V, W, X, Y, and Z, reach their factory in a particular sequence. Y reaches immediately before T but does not immediately follow W. V is the last one to reach. X immediately follows T and is subsequently followed by Z. W reaches before T. Who is the second to reach the factory?
Pankaj, Alpesh, Srikumar, Dinesh, Neeraj and Maninder are sitting in six different rows with one person in each row, exactly one after another. Pankaj is just before Alpesh. Dinesh is sitting in the last row. There are four persons before Alpesh. Srikumar is just after Neeraj. Maninder is not in the first row. Who is sitting just after Maninder?
Seven boxes, A, B, C, D, E, F, and G, are kept one over the other but not necessarily in the same order. Only C is kept above D. Only two boxes are kept between D and F. Only G is kept below A. B is not kept immediately above F. Which box is kept fourth from the top?
A, B, C, M, N, and S live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. Only C lives above B. N lives immediately below B. Only A lives below M. Who lives on floor number 3?
G, H, J, K, L and P live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. Only three people live between P and J, whereas P lives below J. K lives on an odd-numbered floor and immediately above P. G lives on one of the floors below L and on one of the floors above H. Who lives on floor numbered 5?
