Question 20
Let $S$ be the set $\{1, 2, 3, \ldots, 19\}.$ For $a,$ $b \in S,$ define $a \succ b$ to mean that either $0 \lt a - b \le 9$ or $b - a \gt 9.$ How many ordered triples $(x, y, z)$ of elements of $S$ have the property that $x \succ y,$ $y \succ z,$ and $z \succ x?$