Floor Deduction Logic Puzzle Solution
The problem requires us to determine the floor on which person E lives, given a set of conditions about seven people (A, B, C, D, E, F, G) living on seven different floors (numbered 1 to 7).
1. Initial Placements
We start by placing the person whose floor is explicitly given:
- B lives on Floor 3.
2. Determining D's Floor
We use the clue: "Only two persons live between B and D."
- B is on Floor 3.
- To find D's floor, we add 2 floors and 1 position: \(D_{floor} = B_{floor} + 2 + 1 = 3 + 2 + 1 = 6\).
- Therefore, D lives on Floor 6.
3. Determining A's Floor
We use the clue: "Only one person live between D and A."
- D is on Floor 6.
- To find A's floor, we subtract 1 floor and 1 position: \(A_{floor} = D_{floor} - 1 - 1 = 6 - 1 - 1 = 4\).
- Therefore, A lives on Floor 4.
Current Occupancy:
- Floor 3: B
- Floor 4: A
- Floor 6: D
Remaining Floors: 1, 2, 5, 7. People remaining: C, E, F, G.
4. Placing the E-G Pair
We use the clue: "G lives immediately below E."
This means E and G occupy adjacent floors (\(E_{floor} = G_{floor} + 1\)). We check possible placements on the remaining floors (1, 2, 5, 7):
- If E is on Floor 7, G would be on Floor 6 (occupied by D). Impossible.
- If E is on Floor 5, G would be on Floor 4 (occupied by A). Impossible.
- If E is on Floor 2, G would be on Floor 1. This is possible.
Therefore, E lives on Floor 2 and G lives on Floor 1.
5. Placing F and C
We use the clues: "Only one person lives between F and C" and "C does not live on the topmost floor (Floor 7)."
- Occupied floors: G(1), E(2), B(3), A(4), D(6).
- Remaining floors: 5 and 7. People remaining: C and F.
- Floor 6 (occupied by D) lies between floors 5 and 7. This satisfies the condition of one person between F and C.
- Case 1: C on Floor 5, F on Floor 7. This satisfies "one person between F and C". Also, C is not on Floor 7. This arrangement is valid.
- Case 2: C on Floor 7, F on Floor 5. This violates the condition "C does not live on the topmost floor".
Thus, C lives on Floor 5 and F lives on Floor 7.
6. Final Floor Arrangement
The complete arrangement of people on the floors is:
| Floor | Person |
|---|---|
| 7 | F |
| 6 | D |
| 5 | C |
| 4 | A |
| 3 | B |
| 2 | E |
| 1 | G |
7. Conclusion
Based on the deductions, E lives on Floor 2.
Similar Questions
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- Manan, Kiran, Aditi, Isha, Trisha and Arya 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. Trisha lives immediately above Arya. Only one person lives between Arya and Aditi. Only two people live between Isha and Arya. Arya lives on an odd-numbered floor but not on the lowermost floor. Kiran lives immediately above Trisha. Who lives on floor number 2?
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E, F, G, H, L and M 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. Only three people live above G. Only two people live between L and E. Only two people live between M and G. E lives below G but above F. How many people live below H?
- L, K, H, M, Z and U 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. L lives immediately below H. Z lives immediately below U. Only three people live between M and Z. K does not live on the topmost floor. H does not live on any floors below U. How many people live between H and K?
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?
