There are seven friends A, B, C, D, E, F and G living in a seven-floor…
2025
There are seven friends A, B, C, D, E, F and G living in a seven-floor building. The ground floor is numbered 1, the floor above it is numbered 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 on a floor 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.
On which floor does D live?
- A.
5
- B.
6
- C.
4
- D.
3
Attempted by 5 students.
Show answer & explanation
Correct answer: B
Concept
A floor-arrangement puzzle is solved by converting every verbal clue into a numeric constraint - a fixed floor, an odd/even parity rule, an exact vertical distance ('two floors between X and Y' means their floor numbers differ by 3), or a non-adjacency rule ('not immediately above/below' means the floor numbers do not differ by 1). Each remaining case is then tested against the constraints in turn, and any case that produces a contradiction is discarded, until exactly one floor-to-person mapping satisfies every clue simultaneously.
Application
F is fixed on floor 5.
A lives on an odd floor and not on a floor below F, so A must be on floor 7 - the only odd floor at or above 5, since 5 itself is taken by F.
E lives on an odd floor; after F(5) and A(7) are fixed, the remaining odd floors for E are 1 and 3.
Test E = 1: the 'only one person between E and G' clue then fixes G on floor 3 (two floors from E), and the 'two floors between D and E' clue fixes D on floor 4. But floor 4 is immediately above G's floor 3, which breaks the rule that D cannot live immediately above or below G - so this case is rejected.
Test E = 3: G must then be on floor 1 (floor 5 is already taken), and D must be on floor 6 (two floors from E). D(6) and G(1) are not adjacent, so this case survives every check so far.
With G=1, E=3, F=5, D=6 and A=7 fixed, only floors 2 and 4 remain, for B and C - both even, matching the clue that B and C live on even-numbered floors.
The 'two floors between G and C' clue (floors 2 and 3 lying between them) fixes C on floor 4, leaving B on floor 2.
Floor | Person |
|---|---|
7 | A |
6 | D |
5 | F |
4 | C |
3 | E |
2 | B |
1 | G |
Cross-check
Re-checking every original clue against this arrangement confirms it: E(3) is on an odd floor; G(1) is not on the topmost floor; exactly one person, B, lives between E(3) and G(1); A(7) is on an odd floor and not below F(5); D(6) is not immediately above or below G(1); there are two floors between D(6) and E(3); B(2) and C(4) are both on even floors; there are two floors between G(1) and C(4); and F is on floor 5. Every clue holds at once, so the mapping is unique.
D lives on floor 6.