A, B, C, D, E, F, and G are sitting around a circular table facing the centre.
Only C sits between A and E. E sits third to the left of D. B sits to the immediate left of D. G is not an immediate neighbour of E.
How many people sit between C and G when counted from the right of C?
Circular Table Arrangement Puzzle Explained
This problem involves determining the seating arrangement of seven people (A, B, C, D, E, F, G) around a circular table based on given clues. We need to find the number of people between C and G when counting clockwise starting from C's right.
Step 1: Understanding the Constraints
Let's break down the information provided:
- There are 7 people: A, B, C, D, E, F, G.
- They are sitting around a circular table facing the centre.
- Rule 1: Only C sits between A and E. This implies a sequence of either A-C-E or E-C-A along the circle.
- Rule 2: E sits third to the left of D. Since they face the centre, 'left' refers to the clockwise direction. This means there are two people between D and E, with E being clockwise from D. The sequence is D, _, _, E clockwise.
- Rule 3: B sits to the immediate left of D. This means B is directly clockwise to D. The sequence is D-B clockwise.
- Rule 4: G is not an immediate neighbour of E.
Step 2: Determining the Seating Arrangement
We can determine the arrangement step-by-step. Let's denote the positions clockwise as 1, 2, 3, 4, 5, 6, 7.
- Place D: Let's place D at position 1 for reference.
- Place B: According to Rule 3, B is to the immediate left (clockwise) of D. So, B is at position 2. Arrangement: D (1), B (2), _, _, _, _, _
- Place E: According to Rule 2, E is third to the left (clockwise) of D. The first left is position 2 (B). The second left is position 3. The third left is position 4. So, E is at position 4. Arrangement: D (1), B (2), _ (3), E (4), _, _, _
- Place A and C: According to Rule 1, C is between A and E. Since E is at position 4, we have two possibilities for the A-C-E block:
- Possibility 1 (A-C-E clockwise): C would be at position 3 (left of E), and A would be at position 2 (left of C). However, position 2 is already occupied by B. So, this possibility is invalid.
- Possibility 2 (E-C-A clockwise): C would be at position 5 (right of E), and A would be at position 6 (right of C). This fits the available slots.
- Place F and G: The remaining people are F and G, and the remaining positions are 3 and 7. According to Rule 4, G is not an immediate neighbour of E. E is at position 4. Its neighbours are positions 3 and 5. Position 5 is C. Therefore, G cannot be at position 3. This means G must be at position 7. Consequently, F must be at position 3.
Final Arrangement
The final seating arrangement clockwise is:
Position 1: D
Position 2: B
Position 3: F
Position 4: E
Position 5: C
Position 6: A
Position 7: G
Let's verify the conditions:
- A-C-E sequence? Yes, E(4)-C(5)-A(6). C is between A and E.
- E third to the left of D? Yes, D(1) -> Left 1 is B(2), Left 2 is F(3), Left 3 is E(4).
- B immediate left of D? Yes, D(1) -> Left 1 is B(2).
- G not neighbour of E? Yes, E(4)'s neighbours are F(3) and C(5). G is at position 7.
All conditions are satisfied.
Step 3: Answering the Question
The question asks: How many people sit between C and G when counted from the right of C?
- C is at position 5.
- We need to count starting from C's right (counter-clockwise direction).
- The sequence going right (counter-clockwise) from C is: C (Pos 5) -> E (Pos 4) -> F (Pos 3) -> B (Pos 2) -> D (Pos 1) -> G (Pos 7)
- The people sitting between C and G along this path are E, F, B, and D.
- Counting these people: There are 4 people (E, F, B, D).
Therefore, 4 people sit between C and G when counted from the right of C.
Important Questions from Circular Arrangement
P, M, D, A, F, H, R and B are sitting around a circle facing at the centre. R is fourth to the right of A, who is third to the right of P. M is second to the left of H, who is second to the left of P. D is third to the right of B. Which of the following pairs are immediate neighbors of B?
Six people, K, L, M, N, O and P, are sitting on the ground in a hexagonal shape but not necessarily in the same order. K is not sitting next to L or M. N is not sitting next to M or O. L is the neighbour of M. P is in the middle of M and N. What is the correct order of seating positions of the people in clockwise direction?
Six friends, G, H I, J, K and L, are sitting around a circular table, facing towards the centre of the table. H is sitting third to the left of G. L and I are not neighbours of H. K is sitting to the immediate right of I. Who is sitting to the immediate left of L?
Eight friends A, B, C, D, E, F, G and are sitting around a circular table facing each other for a lunch. A is opposite F and third to the right of B. G is between F and D. H is to the left of D. E is between C and A. Who is sitting third to the right of A?
Six friends are sitting at equal distances from each other in a circle and facing the centre of the circle. Diraj is between Pramod and Parthiv. Priyanshu is between Mukund and Laya. Pramod and Mukund are opposite to each other. Laya is to the immediate left of Pramod. Who is sitting to the immediate left of Parthiv?
