Let $\mathbf{M} = \{M\_1, M\_2, ..., M\_s\}$ be a set of (some) 3-element subsets of an $n$-element set. 

It is known that $\forall i,j:\quad 1 \leq i \leq j \leq s: \quad |M\_i\cap M\_j|\neq 1$.

I need to find a maximum $s$ which allows the previous condition to hold. The answer may be dependent on $n$.

I need to solve this task to proceed with my study, but my current math level isn't very good. (But of course I know basic combinatorics). Could you please give as "for dummies" explanation as possible!

Thank you!