This problem requires deductive reasoning to determine the floor arrangement of six residents (A, Q, N, L, R, K) in a 6-floor building.
Floor Arrangement Deductions
We use the given clues to establish the positions:
- Clue 1: A lives on the topmost floor.
- Floor 6: A
- Clue 2: L lives on an even-numbered floor (2, 4) but not the topmost (6).
- Clue 3: K lives immediately above L. This means K and L occupy adjacent floors, with K being on the higher floor. Given L must be on floor 2 or 4, the possible (K, L) pairs are (3, 2) or (5, 4).
- Clue 4: R lives immediately below Q. This means Q and R occupy adjacent floors, with Q being on the higher floor.
- Clue 5: Only three people live between K and N. This implies there are 3 floors between them, meaning K and N are separated by 4 floors (e.g., floor 1 and floor 5).
Determining Floor Positions
Let's test the possible positions for K and L based on Clue 3:
Case 1: L is on Floor 4
- If L is on Floor 4, then K must be on Floor 5 (from Clue 3: K immediately above L).
- Floor 6: A
- Floor 5: K
- Floor 4: L
- Since K is on Floor 5, and there are 3 people between K and N (Clue 5), N must be on Floor 1 (Floors 4, 3, and 2 are between K and N).
- Floor 6: A
- Floor 5: K
- Floor 4: L
- Floor 1: N
- The remaining residents are Q and R, and the remaining floors are 2 and 3.
- R lives immediately below Q (Clue 4). Therefore, Q must be on Floor 3, and R must be on Floor 2.
- Floor 6: A
- Floor 5: K
- Floor 4: L
- Floor 3: Q
- Floor 2: R
- Floor 1: N
- This arrangement satisfies all conditions.
Case 2: L is on Floor 2
- If L is on Floor 2, then K must be on Floor 3 (from Clue 3: K immediately above L).
- Floor 6: A
- Floor 3: K
- Floor 2: L
- If K is on Floor 3, there are no possible positions for N such that exactly 3 people live between them, given the other constraints (A is on 6, L is on 2). For N to be 4 floors away from K (Floor 3), N would need to be on Floor 7 (impossible) or Floor -1 (impossible). This case is invalid.
Conclusion
The only valid arrangement places Q on Floor 3.
Final Arrangement:
- Floor 6: A
- Floor 5: K
- Floor 4: L
- Floor 3: Q
- Floor 2: R
- Floor 1: N
Therefore, Q lives on floor number 3.
Similar Questions
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Important Questions from Floor Puzzle
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Seven boxes, A, B, C, D, E, F, and G, are kept one over the other but not necessarily in the same order. Only C is kept above D. Only two boxes are kept between D and F. Only G is kept below A. B is not kept immediately above F. Which box is kept fourth from the top?
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