A, B, C, D, E and F are sitting around a round table at equal distances. F is sitting opposite to E and is between A and D. C is sitting to the right of E and opposite to A. Who are the neighbours of A?

Introduction / Context:
This problem is a classic circular seating arrangement question. Such questions test your ability to visualise positions around a table and interpret relational clues like “between”, “opposite” and “to the right of”. Here, six people are seated around a round table, and we must carefully use the given information to determine the neighbours of A.

Given Data / Assumptions:
- People: A, B, C, D, E, F are seated around a round table at equal distances.
- F is opposite to E.
- F is between A and D (so A and D are the immediate neighbours of F).
- C is sitting to the right of E and is opposite to A.
- We assume everyone faces the centre, so a persons right is clockwise.

Concept / Approach:
In circular arrangement questions, it is usually best to fix one person at a convenient reference point without loss of generality and then place others step by step using the clues. Opposite positions in a 6-seat circle are exactly three seats apart. The phrase “between A and D” means F has A on one side and D on the other. Combining these constraints with “right of E” and “opposite to A” for C lets us uniquely determine everyone's position and thus identify A's neighbours.

Step-by-Step Solution:
Step 1: Fix A at a reference position on the circle (say at the top). In a 6-seat circle, the seat exactly opposite A is three positions away. Step 2: C is opposite to A, so place C directly opposite A. Step 3: F must sit between A and D, which means F is a direct neighbour of A and also of D. So F can be either the immediate seat to A's left or A's right. Step 4: F is opposite E, so E must be three seats away from F. Consider the two possible positions for F and test which one fits all clues. Step 5: Case 1: Put F on A's right. Then D is next to F on the other side. E would end up opposite F, but then C cannot be both opposite A and to the right of E in a consistent way. This arrangement fails. Step 6: Case 2: Put F on A's left. Then D must sit on F's other side. Now, placing E opposite F makes E two seats clockwise from A. The seat to the right of E is then exactly where C is already placed opposite A, so this arrangement satisfies all clues. Step 7: In this valid arrangement, the two neighbours of A are B on one side and F on the other.

Verification / Alternative check:
Label the seats clockwise as A, B, E, C, D, F. Check clues: F is between A and D (yes), F opposite E (yes), C right of E (moving clockwise from E takes you to C) and C opposite A (yes). Since this arrangement uses all clues consistently, it is correct, and the neighbours of A are indeed B and F.

Why Other Options Are Wrong:
- “F and D”: D is not directly next to A in the valid layout, so this is incorrect.
- “E and F”: E sits two places away from A, not adjacent to A.
- “E and C”: Neither of these is a neighbour of A in the consistent arrangement.

Common Pitfalls:
Students often misinterpret “to the right of” in a circular setting or forget that everyone is assumed to face the centre. Another mistake is not checking all clues after drawing one possible arrangement. The safe approach is to draw neat diagrams for each case and confirm every statement before finalising your answer.

Final Answer:
The neighbours of A around the table are B and F.