Segmenti paralleli

In this article (it’s only in italian, but I’m translating it) I will try to solve some questions about a mathematical problem that my friend Patrizio Frederic, a researcher in statistics at the University of Modena, proposed to me. Given some parallel line segments, is there at least one straight line that passes through all of them? If there were many lines that solve the problem, how can I choose a “better one” among all of them? I fully answer the first question, for the second I’ll just give some ideas for future research.