Question 17
Julián chooses $2007$ points in the plane, no $3$ of them collinear, and draws in red all the segments joining two of these points. Next, Roberto draws several lines. His goal is that every red segment is cut at an interior point by (at least) one of the lines. Determine the smallest $l$ such that, no matter how Julián chooses the $2007$ points, with $l$ suitably chosen lines Roberto surely achieves his goal.