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.

1. Place D: Let's place D at position 1 for reference.
2. 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), _, _, _, _, _
3. 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), _, _, _
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.
   Arrangement: D (1), B (2), _ (3), E (4), C (5), A (6), _ (7)
5. 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.