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Six people P, Q, R, S, T and U live on six different floors of the same building. The bottom-most floor of the building is numbered as 1; the floor above it is numbered as 2 and so on. The topmost floor is numbered as 6. P lives on an even-numbered floor but not on floor number 4. Only two people live between S and P. R lives immediately below T. U lives on an even-numbered floor. Q does not live on the bottom-most floor. How many people live between Q and S?
Three
One
Four
Two
One
Map constraints using the most restrictive variable (P lives on 2 or 6) and place the block (RT) immediately to anchor other positions.
Map constraints using the most restrictive variable (P lives on 2 or 6) and place the block (RT) immediately to anchor other positions.
Placement of P and S
P is on floor 2 or 6 (not 4). If P=2, S must be on 5 (two floors between 2 and 5 are 3,4). If P=6, S must be on 3 (two floors between 6 and 3 are 5,4).
Constraint Checking for R, T, U, and Q
Scenario 1 (P=2, S=5): Remaining floors 1, 3, 4, 6. R and T are consecutive, so they must be 3-4 or 4-5. Since 5 is occupied by S, R and T must be 3 and 4 (T=4, R=3). Remaining are 1 and 6 for U and Q. U is even (6), so U=6. Q=1. This violates the condition that Q is not on floor 1. Scenario 2 (P=6, S=3): Remaining floors 1, 2, 4, 5. R and T are consecutive, so they must be 2-1 (T=2, R=1). Remaining are 4 and 5 for U and Q. U is even (4), so U=4. Q=5. This satisfies all conditions.
Final Floor Arrangement
Floor 6: P, Floor 5: Q, Floor 4: U, Floor 3: S, Floor 2: T, Floor 1: R. Counting people between Q (5) and S (3) is only floor 4 (U), so exactly one person lives between them.
A: Three is incorrect because only one person (U) sits between Q and S. C: Four is incorrect as it exceeds the actual gap found in the arrangement. D: Two is incorrect as it fails to account for the single floor separating the two individuals.
B is correct because the final arrangement places Q on floor 5 and S on floor 3, with U occupying the only floor (4) between them.
In floor-based puzzles, always prioritize placing blocks (like RT) once you have anchored fixed points like 'P is on an even floor but not 4'.