Proving the Impossibility of Non-Intersecting Visitors in a Mathematics Library

[rbzima]

Homework Statement

One afternoon, a mathematics library had several visitors. A librarian noticed that it was impossible to find three visitors so that no two of them met in the library that afternoon. Prove that then it was possible to find two moments of time that afternoon so that each visitor was in the library at one of those two moments.

Homework Equations

None

The Attempt at a Solution

My beef with this question is that it seemingly does not produce enough information. What does several infer?

Here is what I am thinking... Arrange each visitor from $$x_{1}$$ to $$x_{n}$$, but after this I have no idea what to do...

 

[lark]

Several means 3 or more, here.

It isn't true if a person may enter and leave the library more than once in the afternoon.

If you assume that each person enters and leaves the library only once ... say person A is the one who arrives latest, and B is the one who leaves earliest. If A and B overlap, then they're all there between when A arrives and B leaves.

If A and B don't overlap, then divide the people into two groups, depending on whether they overlap with A or with B ... and take it from there.

Laura