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OBM 1987 Problem 4

    Given points A1(x1,y1,z1),A2(x2,y2,z2),..,An(xn,yn,zn)A_1 (x_1, y_1, z_1), A_2 (x_2, y_2, z_2), .., A_n (x_n, y_n, z_n) let P(x,y,z)P (x, y, z) be the point which minimizes Σ(∣x−xi∣+∣y−yi∣+∣z−zi∣)\Sigma ( |x - x_i| + |y -y_i| + |z -z_i| ) . Give an example (for each n>4n > 4 ) of points AiA_i for which the point PP lies outside the convex hull of the points AiA_i .

    Dataset text AI-MO AoPS. Quoted with source.

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