Question 74
For a given integer $n \ge 3$, let $S_1, S_2, \dots, S_m$ be distinct three-element subsets of the set $\{1, 2, \dots, n\}$ such that for each $1 \le i, j \le m; i \ne j$ the sets $S_i \cap S_j$ contain exactly one element. Determine the maximal possible value of $m$ for each $n$.