SEAMO 2019 — Paper E — Grade 9–10 Question 19

For $i=1,\ldots,100$, let $x_i$ be either $\sqrt3-\sqrt2$ or $\sqrt3+\sqrt2$. How many distinct positive integer values can $S=x_1x_2+x_3x_4+\cdots+x_{99}x_{100}$ take?