Question 195
Let $n$ be an integer $\ge 2$. Let $S$ be a set of triples of nonnegative integers $(a, b, c)$ such that $a + b + c = n$ and if $(a, b, c)$ and $(a', b', c')$ are distinct triples in $S$, then $a \ne a'$, $b \ne b'$ and $c \ne c'$. Find the maximum value of $|S|$.