Anuj Bhola Chandan Dilip Eswar Faisal (A) 6 2 5 1 3 4 (B) 2 6 5 1 3 4 (C) 4 2 6 3 1 5 (D) 2 4 6 1 3 5
Building Logic Puzzle Solution
The problem requires finding the correct floor-person combination in a six-storey building based on several constraints.
Constraint Analysis
- Building floors: 1 to 6.
- People: Anuj, Bhola, Chandan, Dilip, Eswar, Faisal.
- Constraint 1: Anuj lives on an even-numbered floor (2, 4, or 6).
- Constraint 2: Bhola does not live on an odd floor (must be on an even floor: 2, 4, or 6).
- Constraint 3: Chandan lives on a higher floor than Faisal (Chandan > Faisal).
- Constraint 4: Dilip does not live on floor 2.
- Constraint 5: Eswar does not live on a floor immediately above or below Bhola (Eswar floor ≠ Bhola floor ± 1).
- Constraint 6: Faisal lives three floors above Dilip (Faisal floor = Dilip floor + 3).
Deduction from Key Constraints
- Faisal and Dilip's Floors: From Constraint 6 (Faisal = Dilip + 3) and Constraint 4 (Dilip ≠ 2), we can determine possible pairs for (Dilip, Faisal):
- If Dilip = 1, Faisal = 1 + 3 = 4. (Valid)
- If Dilip = 3, Faisal = 3 + 3 = 6. (Valid)
- Dilip cannot be 4 or higher, as Faisal would exceed floor 6.
- Anuj and Bhola's Floors: Both Anuj and Bhola must live on even floors (2, 4, 6) from Constraints 1 and 2.
Scenario Evaluation
Scenario 1: Dilip = 3, Faisal = 6
- Floors occupied: 3 (Dilip), 6 (Faisal).
- Remaining floors: 1, 2, 4, 5.
- People remaining: Anuj, Bhola, Chandan, Eswar.
- Anuj and Bhola must occupy two of the remaining even floors {2, 4}.
- Floors 1 and 5 remain for Chandan and Eswar.
- Constraint 3 (Chandan > Faisal): Chandan > 6. This is impossible as the building only has 6 floors.
- Therefore, this scenario is invalid.
Scenario 2: Dilip = 1, Faisal = 4
- Floors occupied: 1 (Dilip), 4 (Faisal).
- Remaining floors: 2, 3, 5, 6.
- People remaining: Anuj, Bhola, Chandan, Eswar.
- Anuj and Bhola must occupy two of the remaining even floors {2, 6} (since floor 4 is taken by Faisal).
- Floors 3 and 5 remain for Chandan and Eswar.
- Constraint 3 (Chandan > Faisal): Chandan > 4. Chandan must be on floor 5 (since 6 is potentially Bhola/Anuj and 3 is too low). So, Chandan = 5.
- This leaves floor 3 for Eswar. So, Eswar = 3.
- Now we have two sub-cases for Anuj and Bhola on floors 2 and 6:
- Sub-case 2a: Anuj = 2, Bhola = 6.
- Combination: A(2), B(6), C(5), D(1), E(3), F(4).
- Check Constraint 5 (Eswar ≠ Bhola ± 1): Eswar is 3, Bhola is 6. 3 ≠ 6 ± 1 (i.e., 3 ≠ 5 or 7). This is valid.
- This yields the combination: Anuj-2, Bhola-6, Chandan-5, Dilip-1, Eswar-3, Faisal-4.
- Sub-case 2b: Anuj = 6, Bhola = 2.
- Combination: A(6), B(2), C(5), D(1), E(3), F(4).
- Check Constraint 5 (Eswar ≠ Bhola ± 1): Eswar is 3, Bhola is 2. 3 ≠ 2 ± 1 (i.e., 3 ≠ 1 or 3). This means Eswar cannot be on floor 3. This contradicts our finding that Eswar must be on floor 3 (since C=5). Therefore, this sub-case is invalid.
- Sub-case 2a: Anuj = 2, Bhola = 6.
- Only Sub-case 2a is valid.
Final Floor-Person Combination
The derived valid combination is:
| Person | Floor |
| Anuj | 2 |
| Bhola | 6 |
| Chandan | 5 |
| Dilip | 1 |
| Eswar | 3 |
| Faisal | 4 |
This corresponds to the sequence (Anuj, Bhola, Chandan, Dilip, Eswar, Faisal) = (2, 6, 5, 1, 3, 4).
Conclusion
Comparing this result with the given options, Option (B) matches the derived correct combination.
Important Questions from Seating Arrangement
- P and Q have been allotted a hostel room with two beds, a study table, and an almirah. P is an avid bird-watcher and wants to sit at the table and watch birds outside the window. Q does not mind that as long as his bed is close to the ceiling fan.
Which one of the following arrangements suits them the most? Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:
• P sits next to S and T.
• Q sits diametrically opposite to P.
• The shortest distance between S and R is equal to the shortest distance between T and U.
Based on the above statements, Q is a neighbor ofSeven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.
Based on the above statements, the only INCORRECT option given below is:- Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:
- P, Q, R, S, T and U are seated around a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true?
