5th All Russian Mathematical Olympiad Problems 1965

5th All Russian Mathematical Olympiad Problems 19651. (a)  Each of x1, ... , xn is -1, 0 or 1. What is the minimal possible value of the sum of all xixj with 1 ≤ i < j ≤ n? (b)  Is the answer the same if the xi are real numbers satisfying 0 ≤ |xi| ≤ 1 for 1 ≤ i ≤ n?