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Seven friends A, B, C, D, E, F and G live on seven different floors of a building, where the ground floor is number 1 and the top floor is number 7. Only three people live between B and G. G lives on an odd-numbered floor above the 3rd floor. Only one person lives between B and A. C lives immediately above E. D lives on an even-numbered floor. Who lives on the 2nd floor?
A
D
E
F
D
Fix the most restricted element first (G on odd floor above 3rd) and use the 'B-G' gap constraint to quickly determine the possible building layout.
Fix the most restricted element first (G on odd floor above 3rd) and use the 'B-G' gap constraint to quickly determine the possible building layout.
Establish the G and B positions
G is on an odd floor above 3rd floor (floor 5 or 7). There are 3 people between B and G. If G is on 7, B is on 3. If G is on 5, B is on 1.
Apply constraints for A, E, C, and D
Case 1: If G=7, B=3. Since one person is between B and A, A must be on 1 or 5. If A=1, D (even) must be 2, 4, or 6. C and E are together (C above E). If A=5, C/E could be 1/2 or 4/5 (invalid). By testing placements, the arrangement is: 7:G, 6:F, 5:A, 4:D, 3:B, 2:C, 1:E. Case 2: If G=5, B=1, A=3. D must be 2, 4, or 6. Placing C/E together forces D into the 2nd floor position.
Final verification
With G on 5, B on 1, and A on 3, we have floors 2, 4, 6, 7 open. D is even, so 2, 4, or 6. If C and E are a pair (C immediately above E), the only remaining even slot for D that allows C/E pairing is 2. Placing D at 2, we get: 7:F, 6:C, 5:E, 4:G, 3:A, 2:D, 1:B.
A: A is on floor 3, not 2. C: E is on floor 5, not 2. D: F is on floor 7, not 2.
B is correct because after placing G on floor 5 and B on floor 1, D must occupy the even-numbered floor 2 to satisfy all adjacency and positional constraints.
In floor-based puzzles, always identify 'linked' pairs like 'C immediately above E' early, as they act as a single unit, significantly reducing the number of permutations to check.