His publisher, Harvard University Press, put out a short video of Lockhart explaining the difference between math and science questions and why he thinks of math as one of the arts, with the help of a nice geometry problem. The video will give you a small taste of what's in store for you in the book.
If you watch the whole video, you'll notice that he never offers an answer for the puzzle he poses (though he suggests that there are many answers). That would be like telling the surprises from the end of a movie. He doesn't give many answers in the book either. He does give lots of hints, and shows lots of strategies and techniques. He knows that the joy of math comes from figuring things out for yourself, so he shows us some of his favorite problems and asks us if we'd like to solve them. But he went beyond a mere compendium of puzzles, and connected the problems he shows, taking his readers on a delightful journey though size and shape (part one) and time and space (part two).
Many of the problems posed are familiar to those who study math, like this one:
And many are less familiar, like this one:
All of them are presented in the context of the larger story Lockhart tells.
You'll find the book enjoyable, even if you're not feeling up to solving these puzzles. But the more often you put down the book and pick up your pen or pencil and paper, the more fun you'll have. I only did a fraction of the problems he posed, so I'm looking forward to lots more fun the second time I read it.