Question 6
At a scientific conference the delegates collectively know $2n$ languages, where $n\ge2$. Each delegate knows exactly two languages, and any two delegates have at most one language in common. For each integer $k$ with $1\le k\le n-1$, there are at most $k-1$ languages each known by at most $k$ delegates. Prove that one can select a group of $2n$ delegates who collectively know all $2n$ languages, with exactly two members of the group knowing each language.