Logic Puzzle: People on Six Floors

The problem requires determining the arrangement of six people (A, G, H, P, S, Y) on six floors (1 to 6) based on given clues and then finding how many people live below person A.

Deduction of Floor Arrangement

Use the given conditions step-by-step:

• Condition 3: "No one lives above G." This places G on the topmost floor, Floor 6.
  • G = Floor 6
• Condition 2: "Only two people live between G and S." Since G is on Floor 6, the arrangement must be G (6), Floor 5, Floor 4, S (3).
  • S = Floor 3
• Condition 4: "H lives below S but above P." This means the order is S > H > P in terms of floor numbers. With S on Floor 3, H must be on Floor 2, and P on Floor 1.
  • H = Floor 2
  • P = Floor 1
• Condition 1: "Only two people live between Y and H." H is on Floor 2. The floors between Y and H must be two distinct floors.
  • If Y were below H, there are no two floors between H (Floor 2) and any floor below it (Floor 1 is occupied by P).
  • Therefore, Y must be above H. The floors available above H are 3, 4, 5. Floor 3 is occupied by S.
  • If Y is on Floor 5, the floors between Y (5) and H (2) are Floor 4 and Floor 3. This satisfies the condition of two people between them.
  • Y = Floor 5
• Placement of A: The only person left is A, and the only floor left is Floor 4.
  • A = Floor 4

Final Floor Arrangement

The determined arrangement from top (6) to bottom (1) is:

Answering the Question

The question asks: "How many people live below A?".

• Person A lives on Floor 4.
• The floors below Floor 4 are Floor 3, Floor 2, and Floor 1.
• The people living on these floors are S, H, and P respectively.
• Therefore, there are 3 people living below A.

Final Answer: Three people live below A.