S, O, R, B, E and T live on six different floors of the same building. The…
2025
S, O, R, B, E and T live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on, till the topmost floor is numbered 6. Only two people live above B. Only E lives between S and O. R lives immediately above T. S lives on one of the floors below R. Who lives on floor number 5?
Answer: B. T — Concept. A floor-arrangement puzzle is solved by working outward from the most restrictive clue, not by guessing an arrangement. Three clue shapes do almost…
- A.
S
- B.
T
- C.
O
- D.
R
Show answer & explanation
Correct answer: B
Concept. A floor-arrangement puzzle is solved by working outward from the most restrictive clue, not by guessing an arrangement. Three clue shapes do almost all the work: "only n people live above P" pins P exactly, because with F floors in all P must stand on floor F - n; "only X lives between P and Q" forces P, X and Q onto three consecutive floors with X in the middle, so they behave as one rigid block; and "R lives immediately above T" forces a rigid pair of adjacent floors. Place the pinned person first, fit the rigid block into whatever consecutive floors remain, then drop the rigid pair into what is left, and use any remaining above/below clue purely as a consistency check.
Application to this question.
The building has six floors, numbered 1 at the bottom up to 6 at the top, and six residents: S, O, R, B, E and T.
Only two people live above B, so exactly two floors lie above B. Therefore B stands on floor 6 - 2 = 4.
Only E lives between S and O, so exactly one resident separates them and that resident is E. S, E and O must therefore occupy three consecutive floors with E in the middle.
Floor 4 is already taken by B, so the runs 2-3-4, 3-4-5 and 4-5-6 are all blocked. The only free run of three consecutive floors is 1-2-3. Hence E stands on floor 2, and S and O take floors 1 and 3 in some order.
Floors 5 and 6 are the only floors still empty, so R and T must fill them. R lives immediately above T, which forces T onto floor 5 and R onto floor 6.
The last clue, S lives on one of the floors below R, is satisfied automatically: S is on floor 1 or 3, and R is on floor 6.
Floor number 5 is therefore occupied by T.
Cross-check.
Floor | Resident |
|---|---|
6 | R |
5 | T |
4 | B |
3 | S or O |
2 | E |
1 | O or S |
Above B on floor 4 there are floors 5 and 6, that is exactly two residents, as required.
S and O stand on floors 1 and 3, and the single floor between them is floor 2, held by E, as required.
R on floor 6 is immediately above T on floor 5, as required.
S on floor 1 or 3 is below R on floor 6, as required.
S and O may swap floors 1 and 3, so the full arrangement is not unique, but floor 5 holds T in both arrangements. The answer to this question is therefore uniquely determined: T.