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Tuesday, October 12, 2010
5th Eötvös Competition Problems 1898
1. For which positive integers n does 3 divide 2n + 1? 2. Triangles ABC, PQR satisfy (1) ∠A = ∠P, (2) |∠B - ∠C| < |∠Q - ∠R|. Show that sin A + sin B + sin C > sin P + sin Q + sin R. What angles A, B, C maximise sin A + sin B + sin C?
