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Problem 4 - Olympiad

Six friends are sitting in a hexagon, with vertices labeled A-F. Riya faces vertex C and sits at vertex D. Tina is opposite Riya. If Sam is two vertices right of Tina, what is Sam's position relative to Riya?

Correct: B

1. Riya at D facing C implies the hexagon is arranged clockwise. 2. Opposite vertex of D is G (invalid). Correction: D's opposite is E. Wait: Hexagon opposite pairs are A-D, B-E, C-F. If Riya is at D, opposite is B. Wait, correction: In a hexagon, opposite vertices are three apart. If Riya is at D, opposite is D +3 = G (invalid). Correct arrangement: If Riya is at D, opposite is G. There's an error here. Let me recalculate. In a hexagon with vertices labeled A-F clockwise: Opposite of A is D, B-E, C-F. If Riya is at D, opposite is G (incorrect). Original label must be 0-indexed as A-F (6 vertices). If Riya is at vertex D (4th), opposite is D + 3 = 7th vertex (G), which is invalid. The problem implies a 6-vertex hexagon labeled A-F clockwise. If Riya is at D (vertex 4), she faces vertex C (vertex 3). This is illogical. Recheck: Facing C means D is the seat. Opposite of D is G. There's ambiguity here. This question has an invalid setup and needs correction.