Question 164
Let $n \ge 4$ be an integer. Define
$$
S = \{(x, y, z) \in \mathbb{Z}^3 \mid xyz = 0 \text{ and } 0 \le x, y, z \lt n\}.
$$
Let $S'$ be the projection of all points in $S$ onto a plane $P$. Given that $|S'| \gt n^2$, determine the least possible value of $|S'|$.
$$
S = \{(x, y, z) \in \mathbb{Z}^3 \mid xyz = 0 \text{ and } 0 \le x, y, z \lt n\}.
$$
Let $S'$ be the projection of all points in $S$ onto a plane $P$. Given that $|S'| \gt n^2$, determine the least possible value of $|S'|$.