A, B, C, D, E and F 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. D lives on an odd-numbered floor but not 3. The sum of floors on which D and E live is 7. A lives immediately below C. F lives on the top floor. How many people live between E and F?
3
Let's solve this step-by-step using the given information:
- F lives on the top floor (6): This is our first definitive placement.
- D lives on an odd-numbered floor but not 3: This means D lives on either floor 1 or 5.
- The sum of floors on which D and E live is 7: This gives us two possibilities:
- If D is on floor 1, E is on floor 6 (6 + 1 = 7).
- If D is on floor 5, E is on floor 2 (5 + 2 = 7).
- A lives immediately below C: This means there is only one floor between A and C.
- Combining information: Since F is on floor 6, and if E were also on floor 6, this would conflict with A and C's arrangement. Therefore, D must be on floor 5, and E must be on floor 2.
- Placing A and C: We know A and C are adjacent. Since E is on floor 2, A and C cannot be placed below floor 2. Given that D is on floor 5, A and C can only be on floors 3 and 4. A is below C, so A is on floor 3 and C is on floor 4.
- Final Floor Arrangement:
- Floor 6: F
- Floor 5: D
- Floor 4: C
- Floor 3: A
- Floor 2: E
- Floor 1: (remaining person)
- People between E and F: Counting from E on floor 2 to F on floor 6, we find 3 people (D, C, and A) live between them.
Therefore, the correct answer is 3.
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