Question 1
Given points $A_1 = (x_1, y_1, z_1)$, $A_2 = (x_2, y_2, z_2)$, ..., $A_n = (x_n, y_n, z_n)$ let $P = (x, y, z)$ be the point which minimizes $\sum_{i=1}^n (|x - x_i| + |y - y_i| + |z - z_i|)$. Give an example (for each $n \gt 4$) of points $A_i$ for which the point $P$ lies outside the convex hull of the points $A_i$.