F, E, R, P, Q and L live on six different floors of the same building. The…
2025
F, E, R, P, Q and L 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 R lives above L. Only E lives below P. How many people live between P and L?
Answer: C. Two — Concept. In a floor puzzle the word "only" makes a clue an exact count, not a mere comparison. "Only X lives above Y" says the number of people above Y is…
- A.
None
- B.
One
- C.
Two
- D.
Four
Show answer & explanation
Correct answer: C
Concept. In a floor puzzle the word "only" makes a clue an exact count, not a mere comparison. "Only X lives above Y" says the number of people above Y is exactly one, which pins Y absolutely: in a building of n floors numbered 1 at the bottom to n at the top, a person with exactly k people above them lives on floor n − k, and a person with exactly k people below them lives on floor k + 1.
Concept (cont.). Once two floors are pinned, the number of people living strictly between floor a and floor b (with a < b) is b − a − 1. That count depends only on the two pinned floors, never on how the still-unplaced people are distributed among the remaining floors.
Application to this arrangement.
Six people occupy six floors, one person per floor, numbered 1 (lowest) up to 6 (topmost).
"Only R lives above L" → exactly one person lives above L, so L is on floor 6 − 1 = 5, and the single person above, R, is on floor 6.
"Only E lives below P" → exactly one person lives below P, so P is on floor 1 + 1 = 2, and the single person below, E, is on floor 1.
Floors 1, 2, 5 and 6 are now occupied by E, P, L and R, so the two people left, F and Q, take the two floors left, 3 and 4, in some order.
Apply the between-count: with P on floor 2 and L on floor 5, the number of people strictly between them is 5 − 2 − 1 = 2 — the residents of floors 3 and 4.
Final arrangement.
Floor | Resident |
|---|---|
6 | R |
5 | L |
4 | F or Q |
3 | Q or F |
2 | P |
1 | E |
Cross-check and contrast.
The two clues fix E, P, L and R uniquely and leave F and Q interchangeable on floors 3 and 4. The arrangement is therefore only partly determined, yet the quantity asked for is fully determined: whichever way F and Q sit, floors 3 and 4 are still the only floors strictly between floor 2 and floor 5, so the count is 2 either way.
Common trap: reading "only R lives above L" as the weaker "R lives above L" would allow L on any floor below R and make the count indeterminate. The word "only" is what converts a comparison into an exact count and pins the floors.
Sanity check on the endpoints: no one lives above R (floor 6) and no one lives below E (floor 1), which is consistent with R being the single person above L and E the single person below P.