There are seven friends A, B, C, D, E, F and G in a seven-floor building. The…
2024
There are seven friends A, B, C, D, E, F and G in a seven-floor building. The ground floor is no. 1, the floor above it is no. 2, and so on.
E does not live on an even-numbered floor. G does not live on the topmost floor. Only one person lives between E and G. A does not live on an even-numbered floor and does not live below F. D does not live immediately above or immediately below G. There are two floors between D and E. Both B and C live on even-numbered floors. There are two floors between G and C. F lives on floor number 5.
How many persons live between E and G?
- A.
1
- B.
2
- C.
3
- D.
4
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: In floor-based (vertical) seating puzzles, each clue is a positional constraint — a parity rule (odd/even floor), a gap rule (“two floors between X and Y” means |X − Y| = 3, i.e. two floors lie strictly in between), a relative rule (‘above’/‘below’), or a forbidden-adjacency rule. Fixing the most constrained entities first, and rejecting any branch that breaks a later clue, converges on the one arrangement that satisfies every clue at once.
F is placed directly: F = floor 5 (given).
A must sit on an odd floor and strictly above F. The only odd floor above 5 is 7, so A = 7.
D and E are separated by two floors (a gap of 3, since two floors lie between them). E must be odd, and floors 5 and 7 are already taken, so E can only be 1 or 3.
If E = 1, then D = 4, and the ‘only one person between E and G’ clue forces G = 3. But then D(4) and G(3) sit on adjacent floors, which breaks the ‘D not immediately above/below G’ clue — so E = 1 is rejected.
So E = 3, giving D = 6 (floors 4 and 5 lie between 3 and 6, satisfying the two-floor gap) — and D(6) is not adjacent to any candidate G, so this branch stays valid.
G is exactly one floor from E(3), so G = 1 or G = 5; floor 5 belongs to F, so G = 1.
B and C must take the two remaining even floors, {2, 4}. The ‘two floors between G and C’ clue needs |G − C| = 3, i.e. C = 4 (since G = 1); B then takes the remaining floor, 2.
Final arrangement:
Floor | Person |
|---|---|
7 | A |
6 | D |
5 | F |
4 | C |
3 | E |
2 | B |
1 | G |
Cross-check against every clue:
E(3) is on an odd floor. ✓
G(1) is not on the topmost floor (7). ✓
Exactly one person (floor 2) lies between E(3) and G(1). ✓
A(7) is on an odd floor and above F(5). ✓
D(6) is not adjacent to G(1). ✓
Two floors (4, 5) lie between D(6) and E(3). ✓
B(2) and C(4) are both on even floors. ✓
Two floors (2, 3) lie between G(1) and C(4). ✓
Answer: Only one person (B, on floor 2) lives between E and G, so the answer is 1.