I’d like to tell you about a nice riddle, which I heard from Bob Krueger (one of our current REU participants, who already has four papers on arXiv!!). The riddle requires very basic linear algebra and is in the spirit of the previous post.

**Riddle.**A library has books and subscribers. Each subscriber read at least one book from the library. Prove that there must exist two

*disjoint*sets of subscribers who read exactly the same books (that is, the union of the books read by the subscribers in each set is the same).

Hint:

**Very**basic linear algebra. Try the first thing that comes to mind.