Students in the Library

Five students visited the library on a certain day. The library is open from 8 AM - 8 PM on all days. Each went for a lunch at some time and returned after it. Any two of them met in the library. Prove that at some moment of time three of them were in the library. Show also that this is not always true for four students.

Hint (posted on July 27, 2005): Draw interval lines for each student for the period during which he was present.