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?