A close polyline $\Delta$ with length $n$ here means a sequence of segments $A_1A_2,\ldots, A_{n-1}A_n$ and $A_nA_1$ so that there are no two segments $A_iA_{i+1}$ and $A_jA_{j+1}$, with $1\leq i,j\leq n$ and $i\neq j$ such that the segments $A_iA_{i+1}$ intersect $A_jA_{j+1}$.
Let $\Delta_1,\Delta_2$ be two close polylines, with length 2016, such that any three lines which contains segments of $\Delta_1,\Delta_2$ are not concurent. The problem state that we always find two segment $AB$, $CD$ where $AB\in \Delta_1$ and $CD\in \Delta_2$ so that $A,B,C,D$ form a convex quadrilateral.
I could prove the question in case $\Delta_1\cap \Delta_2 \neq \emptyset$. But I have no idea for the rest cases.