Question 58
In two endpoints of the main diagonal of the cube numbers $0$ and $2013$ are written, remaining $6$ vertices of the cube contain real numbers $x_1, \dots, x_6$. On each edge of the cube the difference between the numbers at its endpoints is written, $S$ is the sum of squares of the numbers written on the edges. For which numbers $x_1, \dots, x_6$ the value of $S$ is minimal?
