Question 11
a. Each of $x_{1}, \ldots, x_{n}$ is $-1$, $0$ or $1$. What is the minimal possible value of the sum of all $x_{i}x_{j}$ with $1 \leq i \lt j \leq n$?
b. Is the answer the same if the $x_{i}$ are real numbers satisfying $0 \leq |x_{i}| \leq 1$ for $1 \leq i \leq n$?
b. Is the answer the same if the $x_{i}$ are real numbers satisfying $0 \leq |x_{i}| \leq 1$ for $1 \leq i \leq n$?