MathNet 2017-part-04 — 176 problems (EN–VI) Question 123

Let $S = x_1x_2 + x_3x_4 + \dots + x_{2015}x_{2016}$, where $x_1, x_2, \dots, x_{2016} \in \{\sqrt{3} - \sqrt{2}, \sqrt{3} + \sqrt{2}\}$. Is the equality $S = 2016$ possible?