Question 56
Let $T$ denote the 15-element set $T = \{10a+b : 1 \le a \lt b \le 6\}$. Let $S \subseteq T$ be a subset of $T$ in which all 6 digits appear and in which no 3 members exist which contain together all 6 digits 1, 2, ..., 6. Determine the largest possible size $n$ of $S$.