Q, U, I, L, T and S live on six different floors of the same building. The…
2026
Q, U, I, L, T and S live on six different floors of the same building. The lowermost floor is numbered 1, the floor above it is numbered 2, and so on up to the topmost floor, numbered 6.
Exactly two people live between I and S. U is the only person who lives above T. Q lives on an even-numbered floor. I lives on the lowermost floor. How many people live between L and U?
Answer: B. Two — ConceptIn a vertical floor arrangement, place every fixed position first and then use the remaining-floor constraints. If two occupants are on floors a and b,…
- A.
Three
- B.
Two
- C.
Four
- D.
One
Attempted by 21 students.
Show answer & explanation
Correct answer: B
Concept
In a vertical floor arrangement, place every fixed position first and then use the remaining-floor constraints.
If two occupants are on floors a and b, the number of floors strictly between them is |a-b|-1.
Application
I is on the lowermost floor, so I = 1.
Exactly two people are between I and S. Therefore |S-1|-1 = 2, which gives S = 4.
U is the only person above T. With six occupied floors, this fixes T = 5 and U = 6.
Q must be on an even-numbered floor. Floors 4 and 6 are occupied, so Q = 2.
The only unoccupied floor is 3, so L = 3.
Cross-check
The completed arrangement uses each floor exactly once and satisfies every clue:
Floor | Person |
|---|---|
6 | U |
5 | T |
4 | S |
3 | L |
2 | Q |
1 | I |
L is on floor 3 and U is on floor 6. Thus |6-3|-1 = 2; the occupants between them are S and T. Therefore, two people live between L and U.