Question 3
$n$ is a positive integer. $S$ is the set of all triples $(a, b, c)$ such that $1 \leq a, b, c \leq n$. What is the smallest subset $X$ of triples such that for every member of $S$ one can find a member of $X$ which differs in only one position. [For example, for $n = 2$, one could take $X = \{ (1, 1, 1), (2, 2, 2) \}$.]