Ask HN: What books would you give a 16-year old interested in Math?

My son is going to turn 16 in a week. He is a junior (11th grade) in a US High School, and loves math. He participates actively in various math competitions (AMC, ARML and the like), in which he does reasonably well if not at the top. He is taking Calculus now and would like to pursue math major in college.

I want to give him three (or more) math-related books as his birthday present, books that would inspire him, expand his mathematical thinking and introduce him to new concepts. I am also looking for books that won't exceed his current aptitude level too much, lest he might be turned off completely from reading the book. I realize it would be difficult to judge this without knowing him closely, but I hope the information I gave is adequate.

I am not new to HN, but I created a new account specifically to post this question, as I my son is also a HN reader and I don't want tip him off.

I have found a MathOverflow thread (http://mathoverflow.net/questions/8609/favorite-popular-math-book) which gives me some ideas, but I am looking for the collective wisdom of HN readers. Please bear with my indulgence.