Building Arrangement Puzzle Explained

This problem involves placing eight people (P, Q, R, S, T, U, V, W) in a four-storey building. Each floor has two flats, Flat 1 and Flat 2, with Flat 1 being to the left of Flat 2. We need to determine the correct combination based on the given conditions.

Understanding the Constraints

Let's break down the given information:

• Floors are numbered 1 to 4 from bottom to top.
• Each floor has Flat 1 (left) and Flat 2 (right).
• Condition 1: R and S live on the same floor, which is above P's floor.
• Condition 2: Q and R live in the same flat but on different floors.
• Condition 3: P and V do not live in the same flat on different floors.
• Condition 4: P lives on an odd-numbered floor, but not floor 1. This means P lives on Floor 3.
• Condition 5: U lives below the floor on which V lives.
• Condition 6: W does not live on the same floor as P.
• Condition 7: T does not live to the immediate right of P.
• Condition 8: V lives on an even-numbered floor just above Q, and they are in the same flat.

Step-by-Step Deduction

1. Determine P's Floor: From Condition 4, P lives on Floor 3.
2. Analyze V and Q's Placement: Condition 8 states V is on an even floor (Floor 2 or 4) just above Q, in the same flat.
   • If V is on Floor 4, Q must be on Floor 3 (same flat). Since P is also on Floor 3, P and Q must be in different flats.
   • If V is on Floor 2, Q must be on Floor 1 (same flat). This separates P (on F3) from V/Q.
3. Relate Q and R: Condition 2 says Q and R live in the same flat on different floors.
4. Relate R and S: Condition 1 says R and S live on the same floor, above P's floor (Floor 3). This means R and S live on Floor 4.
5. Combine V, Q, R, S, P placements:
   • If V is on Floor 4 (Flat X), then Q is on Floor 3 (Flat X). Since R must be on Floor 4 (with S) and in the same flat as Q (Flat X), R would be on Floor 4 (Flat X). But V is already on Floor 4 (Flat X). This creates a conflict as two people cannot live in the same flat. Therefore, V cannot be on Floor 4.
   • So, V must be on Floor 2, and Q must be on Floor 1, in the same flat (let's call it Flat X).
   • From Condition 2, R lives in the same flat (Flat X) as Q but on a different floor. Since R and S are on Floor 4, R must be on Floor 4 (Flat X).
   • This means Q is on F1-FlatX, V is on F2-FlatX, and R is on F4-FlatX.
   • S lives on Floor 4 with R, so S must be in the other flat on Floor 4 (Flat Y).
   • P lives on Floor 3. Condition 3 states P and V do not live in the same flat. Since V is in Flat X, P cannot be in Flat X. P must be in Flat Y on Floor 3.
   • So, we have: Q (F1-FlatX), V (F2-FlatX), P (F3-FlatY), R (F4-FlatX), S (F4-FlatY).
   • Assigning Flat 1 and Flat 2: Let FlatX be Flat 1 and FlatY be Flat 2.
     • Q lives on F1-Flat 1.
     • V lives on F2-Flat 1.
     • P lives on F3-Flat 2.
     • R lives on F4-Flat 1.
     • S lives on F4-Flat 2.
6. Place U: Condition 5 states U lives below V (F2-Flat 1). U can be on Floor 1 in either Flat 1 or Flat 2. Since Q is in F1-Flat 1, U must be in F1-Flat 2.
7. Place W: Condition 6 states W does not live on the same floor as P (Floor 3). The remaining flats are F2-Flat 2 and F3-Flat 1. Since W cannot be on Floor 3, W must be on F2-Flat 2.
8. Place T: The only remaining person is T, and the only remaining flat is F3-Flat 1.

Final Arrangement

Based on the deductions, the final arrangement is:

Evaluating the Options

Let's check the given combinations against our final arrangement:

• 1. Floor 4 - Flat 1 - S: Incorrect. S is on Floor 4, Flat 2.
• 2. Floor 2 - Flat 1 - V: Correct. V is indeed on Floor 2, Flat 1.
• 3. Floor 1 - Flat 2 - W: Incorrect. W is on Floor 2, Flat 2. U is on Floor 1, Flat 2.
• 4. Floor 3 - Flat 2 - T: Incorrect. T is on Floor 3, Flat 1. P is on Floor 3, Flat 2.
• 5. Floor 1 - Flat 1 - V: Incorrect. V is on Floor 2, Flat 1. Q is on Floor 1, Flat 1.

Therefore, the only true combination is Floor 2 - Flat 1 - V.