Building Logic Puzzle Analysis
We need to determine the vacant floor in a seven-storey building based on the given clues about residents A, B, C, D, E, and F.
Key Information and Initial Deductions
- Building floors: 1 to 7.
- Residents: A, B, C, D, E, F (6 people).
- One floor is vacant.
- Resident B lives on floor 6.
- Floors 1 and 2 are occupied (No floor below floor 3 is vacant).
- Odd-numbered floors (1, 3, 5, 7) are occupied (No odd numbered floor is vacant).
Combining the occupancy rules:
- Floors 1 and 2 are occupied.
- Floors 1, 3, 5, 7 are occupied.
- Therefore, floors 1, 2, 3, 5, 7 are definitely occupied.
- Resident B is on floor 6.
- This means floors 1, 2, 3, 5, 6, 7 are occupied.
- The only remaining floor is 4. Thus, floor 4 must be the vacant floor.
Let's verify this by checking the remaining conditions:
Resident Placement Verification
Condition: Only B lives between A and F
Since B is on floor 6, A and F must be on the floors immediately above and below B, which are floors 5 and 7 (in any order).
Condition: Only two people live between C and F, and C lives below F
This implies the difference between F's floor and C's floor is 3 (e.g., C, P1, P2, F).
- Case 1: F is on floor 7. Then C must be on floor $7 - 3 = 4$. C lives on floor 4. This contradicts our deduction that floor 4 is vacant. So, F cannot be on floor 7.
- Case 2: F is on floor 5. Then C must be on floor $5 - 3 = 2$. C lives on floor 2. This is consistent, as floor 2 must be occupied.
Therefore, F is on floor 5, and C is on floor 2.
Current placements:
- C: Floor 2
- F: Floor 5
- B: Floor 6
- A: Floor 7 (since F is on 5)
Condition: More than one person lives between D and B
B is on floor 6. D cannot be on floor 5 (F) or floor 7 (A). D cannot be on floor 2 (C). Possible floors for D are 1 or 3 or 4.
- If D is on floor 4, the gap between D and B is 1 person (F on 5). This violates the condition. So D cannot be on floor 4.
- If D is on floor 3, the gap between D and B includes floor 4 (vacant) and floor 5 (F). This satisfies "more than one".
- If D is on floor 1, the gap between D and B includes floors 2(C), 3, 4(vacant), 5(F). This satisfies "more than one".
So, D is either on floor 1 or floor 3.
Condition: Only one person lives between E and D
This implies the difference between E's floor and D's floor is 2 (e.g., E, P1, D).
- If D is on floor 3: E must be on floor 1 (to have C on floor 2 between them). Occupants: E(1), C(2), D(3), F(5), B(6), A(7). Floor 4 is vacant. This configuration works.
- If D is on floor 1: E must be on floor 3 (to have C on floor 2 between them). Occupants: D(1), C(2), E(3), F(5), B(6), A(7). Floor 4 is vacant. This configuration also works.
Final Conclusion
In both valid scenarios derived from the conditions, the set of occupied floors includes 1, 2, 3, 5, 6, and 7, leaving floor 4 as the vacant floor. All conditions are met with floor 4 being vacant.
Similar Questions
- Seven persons P, Q, R, S, T, U and W live on different floors in a building having seven floors (first floor is the lowermost floor, then second floor is above it and then so on). Only one person lives on one floor. P lives on one of the floor above S and S does not live on an odd numbered floor. Only two persons live between S and T. U lives immediately above W. Only four persons live between T and P.
Who are the neighbours of P? Read the following information carefully and answer the question that follows.
Five coaching classes — P, Q, R, S, and T — are located on five different floors numbered 1, 2, 3, 4, and 5, but not necessarily in the same order. Each coaching class teaches only one of the following subjects: Physics, Chemistry, Mathematics, Biology, and English, but not necessarily in the same order.- Class S teaches Biology, while class Q does not teach English.
- Class R is located on the third floor, and class P teaches Chemistry.
- The class located on the fifth floor teaches Physics.
- The class located on the third floor does not teach English or Physics.
Based on the above information, determine on which floor Mathematics is taught.
- Read the given information carefully and answer the question that follows.
Five coaching classes P,Q,R,S and $\mathrm{T}$ are located on five different floors $1, 2, 3, 4$ and $5$, not necessarily in the same order. Only one subject out of Physics, Chemistry, Mathematics, Biology and English, is taught in each coaching class, but not necessarily in the same order.
The following information is also known:- Biology is taught in coaching class S, while English is not taught in coaching class Q.
- Coaching class R is on the $3^{\text{rd}}$ floor, and Chemistry is taught in coaching class P.
- Physics is taught in the coaching class on the $5^{\text{th}}$ floor.
- The coaching class on the $3^{\text{rd}}$ floor does not teach either English or Physics.
On the basis of the information given, identify the floor on which Mathematics is taught. - Six companies, P, Q, R, S, T and U, are situated on different floors of a 6-floored building, but not necessarily in the same order. The lowest floor of the building is numbered 1, the floor above it is numbered as 2, and so on, up to the top floor, which is numbered as 6. Company Q is not situated at floor number 1. Company P has five companies situated below its floor. There are only two companies situated between the floors of companies T and P and also between the companies Q and U. Company S is situated on an odd numbered floor, but not on the lowest floor. Which company is situated on floor number 1?
- Anu lives on one floor in a seven storey building. Each floor of the building is numbered in a manner that the lowest floor is numbered as one and the highest floor is numbered as seven. She does not live on an even numbered floor. At least two floors are above and two floors are below the floor where she lives. There are at least two floors between her and her friend who lives on the topmost floor. On which floor is Anu's flat?
- Six friends Amit, Vinay, Rajiv, Mukul, Chetan and David are living on six different floors of the same building. The lowermost floor of the building is numbered 1, the floor above it is numbered 2, and so on till the topmost floor is numbered 6. No two friends live on the same floor. Vinay lives on the floor immediately above the floor on which Rajiv lives. Mukul lives on floor number 4. Amit lives on an even numbered floor. Chetan lives on floor number 1. Vinay does not live on floor number 6.
On which floor number does David live? A building has seven floors numbered one to seven in such a manner that the ground floor is numbered one, the floor above it is numbered two, and so on, such that the topmost floor is numbered seven. One of the seven persons, namely T, U, V, W, X, Y, and Z, lives on each floor, but not necessarily in the same order.
There are only two people living between the floors of X and Z. No person lives above U's floor. T lives in one of the odd floors. The number of people living above and below Y is equal. W does not live above anyone other than V. X lives in one of the floors above Z.
Who lives on the $5^{\text{th}}$ floor?
- In a building, there were a total of seven floors. The floors were numbered 1 to 7 from bottom to top, floor 1 being the ground floor. Each of the 7 men among A, B, C, D, E, F and G, occupied a floor, not necessarily in the same order. G occupied floor number 4. Only one person lived below the floor occupied by E. B was exactly above A. C was exactly below G. F occupied the topmost floor. Which man occupied floor 1?
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?
