Six friends - A, B, C, D, E and F - are sitting around a circular table, facing towards the centre of the table. D and C are immediate neighbours of A. B is second to the right of A. F is an immediate neighbour of E, and fourth to the left of D. What is the position of E?
- AThird to the left of A
- BImmediate left of C
- CSecond to the right of A
- DImmediate neighbour of D and F
Solution & Step-by-step Explanation
Let us arrange the six friends in 6 numbered spots around a circular table (positions 0 to 5 in a counter-clockwise direction), facing inward towards the center:
1. Place A at spot .
2. "B is second to the right of A." Facing the center, right is counter-clockwise. Therefore, B sits at spot .
3. "D and C are immediate neighbours of A." This means D and C must occupy spots and in some order.
4. "F is fourth to the left of D." Facing the center, left means moving in a clockwise direction.
* If D is placed at spot , fourth to its left (clockwise) would be spot , which is already reserved for C. This causes a contradiction.
* Therefore, D must be at spot , which leaves C at spot .
5. Now finding F's position: D is at spot . Fourth to the left of spot (moving clockwise: ) is spot . So, F sits at spot .
6. The only remaining empty spot is , which must be occupied by E.
Let us verify: "F is an immediate neighbour of E." F is at and E is at , so they are neighbors. The arrangement holds true.
Final Positions (Counter-Clockwise):
* Spot 0: A
* Spot 1: D
* Spot 2: B
* Spot 3: F
* Spot 4: E
* Spot 5: C
Analyzing the options for E (at spot 4):
* Spot 5 is occupied by C. Facing the center from spot 5, clockwise (immediate left) leads to spot 4. Thus, E is to the immediate left of C.
1. Place A at spot .
2. "B is second to the right of A." Facing the center, right is counter-clockwise. Therefore, B sits at spot .
3. "D and C are immediate neighbours of A." This means D and C must occupy spots and in some order.
4. "F is fourth to the left of D." Facing the center, left means moving in a clockwise direction.
* If D is placed at spot , fourth to its left (clockwise) would be spot , which is already reserved for C. This causes a contradiction.
* Therefore, D must be at spot , which leaves C at spot .
5. Now finding F's position: D is at spot . Fourth to the left of spot (moving clockwise: ) is spot . So, F sits at spot .
6. The only remaining empty spot is , which must be occupied by E.
Let us verify: "F is an immediate neighbour of E." F is at and E is at , so they are neighbors. The arrangement holds true.
Final Positions (Counter-Clockwise):
* Spot 0: A
* Spot 1: D
* Spot 2: B
* Spot 3: F
* Spot 4: E
* Spot 5: C
Analyzing the options for E (at spot 4):
* Spot 5 is occupied by C. Facing the center from spot 5, clockwise (immediate left) leads to spot 4. Thus, E is to the immediate left of C.