Six persons A, B, C, D, E, and F live on six different floors of the same building. The bottommost floor is the first, the floor above it is the second, and so on up to the sixth floor at the top. A lives on an odd numbered floor. C lives immediately below A. There is a gap of exactly two floors between the floors of C and F. D lives immediately above F. B lives above E, and E lives below F. How many persons live on floors below E?

Introduction / Context:
This is a floor arrangement puzzle involving six people and six floors. Several relational clues are given about who lives immediately above, immediately below, or with a fixed gap in between floors. The task is to determine exactly how many people live below E once all constraints are satisfied. Such puzzles test systematic reasoning and careful handling of multiple interdependent conditions.

Given Data / Assumptions:

• The building has six floors, numbered 1 (bottom) to 6 (top).
• Persons: A, B, C, D, E, F. Each occupies a distinct floor.
• A lives on an odd numbered floor.
• C lives immediately below A.
• There is a gap of exactly two floors between the floors of C and F, so the difference in floor numbers is 3.
• D lives immediately above F.
• B lives above E.
• E lives below F.

Concept / Approach:
The best way is to use the constraints that involve immediate above and below relations and fixed gaps, because they strongly restrict positions. A and C are consecutive, and F and D are consecutive. There is also a three floor separation between C and F. Starting with the possible positions for A and C, we can deduce F and D, then place E and B while respecting the above and below conditions. Once a valid arrangement is found, we can answer the question about how many persons live below E.

Step-by-Step Solution:
Step 1: A lives on an odd floor, so A can be on floor 1, 3, or 5.Step 2: C lives immediately below A. Therefore, if A is on floor 1, C would be on floor 0, which is impossible. So A cannot be on floor 1.Step 3: If A is on floor 3, then C is on floor 2. If A is on floor 5, then C is on floor 4.Step 4: There is a gap of exactly two floors between C and F, so the difference between their floor numbers is 3. Consider case 1: C on floor 2 (so A on floor 3). Then F must be on floor 5 (since 2 + 3 = 5 is valid, while 2 − 3 is not).Step 5: D lives immediately above F, so if F is on floor 5, D must be on floor 6.Step 6: Now we have A on 3, C on 2, F on 5, and D on 6. The remaining floors 1 and 4 must be occupied by B and E, subject to B living above E and E living below F.Step 7: Since F is on floor 5, E must be on a floor below 5. Among the remaining floors 1 and 4, both are below 5.Step 8: B must be above E. If we place E on floor 1, B can then be on floor 4. This satisfies B above E and E below F. If we tried E on floor 4, B would need to be on a floor higher than 4, but floors 5 and 6 are already occupied by F and D, so that is impossible.Step 9: Therefore, E is on floor 1 and B is on floor 4 in this valid arrangement.Step 10: Now check the alternative case 2 where A is on floor 5 and C on floor 4. Then the floor of F would need to be 1 (since 4 − 3 = 1), but then E must be below F, which is impossible because there is no floor below 1. Hence case 2 is invalid.

Verification / Alternative check:

Why Other Options Are Wrong:

• Option B (1 person below E), C (2 persons), D (3 persons), and E (4 persons) all require E to be on a higher floor. This contradicts the unique valid arrangement in which E is on the first floor.
• Any arrangement putting E above floor 1 either violates B above E or E below F, or clashes with the fixed positions of A, C, F, and D.

Common Pitfalls:

• Not checking all possible positions for A and thereby missing that A cannot be on the first floor.
• Forgetting that the floor gap condition between C and F is three floors, not two floors between them in the sense of only two people between.
• Trying to place E on floor 4 without noticing that there is no available floor above 4 left for B.

Final Answer:
The number of persons living below E is 0.