i) There are 9 friends A, B, C, D, E, F, G, H seated in a circle...

1. Identify the Core Conflict The question states there are 9 friends listed as A, B, C, D, E, F, G, H. However, the list provided only contains 8 letters. This missing ninth person creates immediate ambiguity for a fixed circular arrangement. 2. Analyze Seating Constraints Based on the provided rules: - Adjacency: The pairs AC, DG, HE, and FB must sit next to each other. - A and H: These two must also be seated adjacent to each other. - H and B: B is positioned 2 nd to the right of H. - C and E: E is positioned 3rd to the right of C. 3. Test for Consistency When attempting to place these individuals in a circle: - If A is adjacent to both C and H , the sequence must be ($\mathrm{C}-\mathrm{A}-\mathrm{H}$). - Since $B$ is 2 nd to the right of $H$, and $A$ is already to the left of $H, B$ must be one seat away from $H$ in the clockwise direction. - However, the pair FB must be adjacent, and HE must be adjacent. - The constraint that ($\mathrm{E}$) is ($\mathrm{3 r d}$) to the right of ($\mathrm{C}$) must also be satisfied while maintaining all other adjacency pairs (DG, FB, etc.). Conclusion Because there is a discrepancy in the number of friends ( 9 mentioned vs. 8 listed) and the specific seating constraints for the 9 th position are unknown, the exact relative position of everyone-specifically who is 2 nd to the left of A-cannot be uniquely fixed. Correct Answer: (D) Cannot be determined