There are books everywhere in my house. Seriously. Instead of knick-knacks, we have books. Some are old and no longer read. Some are reference types left over from my college days or when our daughter was being home educated. Some are for my own writing -- research books, writing books, a thesaurus. Some are beloved favorites that have been read again and again. Some are in various to-be-read piles -- purchased to be read, but not gotten to just yet.
While I've never been to an island of any type — deserted or not — I have been known to take books to the beach. As a child I remember reading the Raggedy Ann Stories at my grandparents cabin. That was more interesting to me then fishing or swimming in the lake. It was the same scenario, different books, when I lived in the Tidewater area of Virginia. Driving to the beach for the day was nothing and books were a constant companion.
So, to get back to the question, I have no idea! I read books so quickly that three wouldn't last me long. There are classics I've never read (though I'm currently listening to The Three Musketeers by Alexandar Dumas on my iPod during my morning walks). There are classics I want to re-read (let's not discuss the number of times I've read Island of the Blue Dolphins by Scott O'Dell). There are a number of series I enjoy (Mrs. Jefferies by Emily Brightwell, for example). There are authors who I love to read (including but not limited to Jan Burke and Charlane Harris). I can't pick three!!
Would it be cheating to require my deserted island to have electricity and internet capabilities? Because then I'll just take my Sony e-book reader and save myself a who lot of worry! Otherwise, I guess I'll spend this winter in the Black Hills of South Dakota. At least then I can have more than three books...