This problem involves determining the occupants of six floors based on a set of logical conditions. We need to find who lives on the topmost floor (floor 6).

Floor Arrangement Constraints

• Floors are numbered 1 (lowest) to 6 (topmost).
• Six people: A, G, H, P, S, Y.
• Condition 1: H lives immediately above Y (\(H = Y + 1\)).
• Condition 2: Exactly two people live between P and Y (\(|P - Y| = 3\)).
• Condition 3: P lives on an odd-numbered floor (1, 3, or 5).
• Condition 4: S lives immediately below G (\(S = G - 1\)).

Step-by-Step Deduction

1. Analyze P's position: P must be on an odd floor (1, 3, or 5).
   • If P is on floor 5: Y must be on floor \(5 - 3 = 2\). H must be on floor \(2 + 1 = 3\). Floors occupied: P(5), Y(2), H(3). Remaining floors: 1, 4, 6. Remaining people: A, G, S. Condition \(S = G - 1\) requires two adjacent floors. The remaining floors (1, 4, 6) do not contain an adjacent pair. This case is impossible.
   • If P is on floor 3: Y could be on floor \(3 + 3 = 6\). H would need to be on floor \(6 + 1 = 7\), which is impossible. Y cannot be on floor \(3 - 3 = 0\). This case is impossible.
   • If P is on floor 1: Y must be on floor \(1 + 3 = 4\). H must be on floor \(4 + 1 = 5\). Floors occupied: P(1), Y(4), H(5). Remaining floors: 2, 3, 6. Remaining people: A, G, S.
2. Place S and G: With P(1), Y(4), H(5), we need to place A, G, S on floors 2, 3, 6. Condition \(S = G - 1\) requires S and G to be on adjacent floors. The only available adjacent floors are 2 and 3. Since S lives below G, S must be on floor 2 and G on floor 3. Floors occupied: P(1), S(2), G(3), Y(4), H(5).
3. Determine occupant of floor 6: The only remaining person is A, and the only remaining floor is 6. Therefore, A lives on floor 6.

Final Floor Arrangement

The topmost floor is floor 6, and A lives there.