I think [Problem-Solving Strategy][1] is an interesting book for teens. It does not need a deep mathematical background. However, if its math is too hard you can find an interesting and small book about discrete mathematics¹ to read first and then switch back to this book. I read it when I was in high school and this book motivated me to do stuff in CS.

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 1. I think what constitutes a discrete mathematics book for teens depends on native culture and language. I know a good one in my language, but I do not know any good ones in other languages.

  [1]: http://www.amazon.com/Problem-Solving-Strategies-Problem-Books-Mathematics/dp/0387982191