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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 numbered 1 and the top floor is numbered 7. D lives on an odd-numbered floor above the 4th floor. Only two people live between D and B. A lives immediately above G. F lives on an even-numbered floor. E lives below C. Who lives on the 2nd floor?
B
E
F
G
F
Identify the extreme position first (D on floor 7 or 5) and use the linked pair (A, G) to anchor the remaining floor slots.
Identify the extreme position first (D on floor 7 or 5) and use the linked pair (A, G) to anchor the remaining floor slots.
Establish the floor constraints
D is on an odd floor above 4 (5 or 7). If D is at 7, B must be at 4. If D is at 5, B must be at 2 or 8 (invalid). Let us test D=7, then B=4. Remaining floors are 1, 2, 3, 5, 6.
Place A and G
A lives immediately above G (AG block). With floors 1, 2, 3, 5, 6 open, the only place for AG block is 6 and 5 or 3 and 2. If AG is 6,5, then floors 1, 2, 3 remain for C, E, F. F must be even (floor 2). SoF=2, which leaves 1 and 3 for C and E. Since E is below C, C=3, E=1. This satisfies all conditions.
Verify final arrangement
Floor 7: D, Floor 6: A, Floor 5: G, Floor 4: B, Floor 3: C, Floor 2: F, Floor 1: E. This satisfies all constraints: D is odd above 4; Two between D(7) and B(4); A above G; F is even (2); E is below C.
A: B is on floor 4, not floor 2. B: E is on floor 1, not floor 2. D: G is on floor 5, not floor 2.
C is correct because our step-by-step constraint satisfaction leads to F occupying the 2nd floor, satisfying all given conditions.
In floor-based puzzles, always place the entity with the most specific constraint (like 'D lives above 4') first to minimize trial-and-error.