RU-ALLRUSSIAN 1969 Problem 7

Given n points in space such that the triangle formed from any three of the points has an angle greater than 120 degrees. Prove that the points can be labeled 1, 2, 3, ..., n so that the angle defined by i, $\mathrm{i} + 1$ , $\mathrm{i} + 2$ is greater than 120 degrees for $\mathrm{i} = 1,2,\ldots ,\mathrm{n} - 2$ .