MathNet 2017-part-06 — 176 problems (EN–VI) Question 9

Let $S = \{-17, -16, \ldots, 16, 17\}$. We call a subset $T$ of $S$ a good set if $-x \in T$ for any $x \in T$ and if $x, y, z \in T$ ($x, y, z$ may be equal) then $x + y + z \neq 0$. Find the largest number of elements in a good set.