RU-ALLRUSSIAN 1990 Problem 16

Given a point X and n vectors $\mathbf{x}_{\mathrm{i}}$ with sum zero in the plane. For each permutation of the vectors we form a set of n points, by starting at X and adding the vectors in order. For example, with the original ordering we get $\mathbf{X}_{1}$ such that $\mathbf{X}\mathbf{X}_{1} = \mathbf{x}_{1}$ , $\mathbf{X}_{2}$ such that $\mathbf{X}_{1}\mathbf{X}_{2} = \mathbf{x}_{2}$ and so on. Show that for some permutation we can find two points Y, Z with angle $\mathbf{Y}\mathbf{X}\mathbf{Z} = 60$ deg, so that all the points lie inside or on the triangle XYZ.