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Six people M, N, O, P, Q, and R live on six different floors of the same building. The lowermost floor is numbered 1 and the topmost is 6. M lives on an even-numbered floor. Only two people live between M and R. O lives immediately above Q. P lives on the floor immediately below R. Who lives on the topmost floor?
M
N
O
Q
M
Place the most constrained items first: R, P, and the gap between M and R. Use the O-Q block as a rigid unit to fill the remaining slots.
Place the most constrained items first: R, P, and the gap between M and R. Use the O-Q block as a rigid unit to fill the remaining slots.
Establish R and P placement
M lives on an even floor (2, 4, or 6). There are two people between M and R. P is immediately below R. If M is on floor 6, R is on floor 3, and P is on floor 2. If M is on floor 4, R is on floor 1, but P cannot be below R. If M is on floor 2, R is on floor 5, and P is on floor 4.
Placement of O and Q
Using the scenario where M is on floor 6: R is on floor 3, P is on floor 2. Floors 1, 4, and 5 are empty. O is immediately above Q, which fits only on floors 5 and 4. This leaves floor 1 for N. The final order is 6-M, 5-O, 4-Q, 3-R, 2-P, 1-N.
Final Verification
M (6, even) is two floors away from R (3). O (5) is immediately above Q (4). P (2) is immediately below R (3). All constraints are satisfied.
B: N must live on floor 1, not the top. C: O lives on floor 5, not the top. D: Q lives on floor 4, not the top.
A is correct because placing M on floor 6 allows for the valid arrangement M-O-Q-R-P-N where M is at the top.
In floor-based puzzles, always look for the 'immediately above/below' block first, as it acts as a fixed anchor to test your scenarios.