MathNet 2010 — Part 02 Question 138

Determine all possible values of positive integer $n$, such that there are $n$ different 3-element subsets $A_1, A_2, \dots, A_n$ of the set $\{1, 2, \dots, n\}$, with $|A_i \cap A_j| \neq 1$ for all $i \neq j$.