RU-ALLRUSSIAN 1965 Problem 1

(a) Each of $\mathbf{x}_{1}, \ldots , \mathbf{x}_{\mathrm{n}}$ is -1, 0 or 1. What is the minimal possible value of the sum of all $\mathbf{x}_{i}\mathbf{x}_{j}$ with $1 \leq = \mathrm{i} < \mathrm{j} \leq = \mathrm{n}$ ? (b) Is the answer the same if the $\mathbf{x}_{i}$ are real numbers satisfying $0 \leq = |\mathbf{x}_{i}| \leq = 1$ for $1 \leq = \mathrm{i} \leq = \mathrm{n}$ ?