Problem

Source: Turkey EGMO TST 2014 P6

Tags: combinatorics



For a given integer $n\ge3$, let $S_1, S_2,\ldots,S_m$ be distinct three-element subsets of the set $\{1,2,\ldots,n\}$ such that for each $1\le i,j\le m; i\neq j$ the sets $S_i\cap S_j$ contain exactly one element. Determine the maximal possible value of $m$ for each $n$.