T, A, R, G, U and S live on six different floors of the same building. The…
2026
T, A, R, G, U and S live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. S lives on the floor numbered 4. Only two people live between S and G. Only T lives between S and U. A lives immediately below S. Who lives on floor number 2?
Answer: D. R — Concept. A floor puzzle is a number line: the floors run from 1 at the bottom to 6 at the top, so every positional clue can be rewritten as arithmetic on…
- A.
T
- B.
S
- C.
U
- D.
R
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Correct answer: D
Concept. A floor puzzle is a number line: the floors run from 1 at the bottom to 6 at the top, so every positional clue can be rewritten as arithmetic on floor numbers. Two clue forms do all the work. "Exactly k people live between X and Y" means k floors lie in the gap, so the difference of the two floor numbers is k + 1, with the direction left open. "Immediately below (or above)" means that difference is 1. The method follows: start from the clue that names an absolute floor, turn every other clue into such a difference, drop each branch that leaves the range 1 to 6 or lands on a floor already taken, and read the remaining person into the remaining floor.
Application. The clues are applied in the order that fixes the most positions first.
S is placed outright by the stem: S lives on floor 4.
"Only two people live between S and G" puts two floors in the gap, so the difference is 3: G is on floor 4 - 3 = 1 or on floor 4 + 3 = 7. The building ends at floor 6, so G lives on floor 1.
"A lives immediately below S" makes the difference 1 downwards, so A lives on floor 4 - 1 = 3.
"Only T lives between S and U" puts one floor in the gap and names T as its occupant, so the difference between S and U is 2: either U on floor 6 with T on floor 5, or U on floor 2 with T on floor 3.
Floor 3 is already occupied by A, so the branch with T on floor 3 collapses. Hence U lives on floor 6 and T lives on floor 5.
Floors 1, 3, 4, 5 and 6 now hold G, A, S, T and U. R is the one person still unplaced and floor 2 is the one floor still empty, so R lives on floor 2.
Cross-check. The completed arrangement reads:
Floor | Resident |
|---|---|
6 | U |
5 | T |
4 | S |
3 | A |
2 | R |
1 | G |
S is on floor 4, exactly as the stem states.
Between G on floor 1 and S on floor 4 lie floors 2 and 3, that is two people - no more and no fewer.
Between S on floor 4 and U on floor 6 lies floor 5 alone, and T occupies it, so T is the one person in that gap.
A on floor 3 sits immediately below S on floor 4.
All four clues hold in this single arrangement, so the person living on floor number 2 is R.