I would like to use a puzzle in my game which I found in a book. Is this legal? Do I have to credit the book?

If it isn't covered in the book or the publisher's web site already, the best thing is to contact the people who made the book and get permission. Start with an email to the author or publisher. Often authors will give written permission in a quick email if you ask in a polite email describing your intentions.

Without actual permission it is a legal risk. The degree of risk and the costs of those risks depend on many factors, including how much of the book is devoted to the puzzle, and how much they want to protect it.  For instance, if the entire book was devoted to the puzzle and they were making a lot of money from the book, you'd probably get a legal demand rather quickly. If the puzzle were a tiny part of the book and the book was nearing end of life with no sequel planned, legal risks are low.  But we don't know those details.

It is up to you (and your lawyer) how much legal risk you are willing to take. 

This book is a "compilation" of puzzles. This means that authors themselves state that they are NOT original creators of the content they published. They only "compiled" it from various sources.

1 hour ago, Thal said:

This book is a "compilation" of puzzles. This means that authors themselves state that they are NOT original creators of the content they published. They only "compiled" it from various sources.

If I were you, not only would I ask permission, but I'd offer to the give credit to the book and the authors in my game.

Giving credit to the book and authors is a form of compensation.

One of the beginning rules of negotiation is to never negotiate against yourself. When asking about using it, that means not mentioning credit or anything up front, wait until they respond that they're receptive, and that they're interested in negotiating something. It may be that no credit is needed, or in some cases, credit is unwanted.

As someone with bookshelves full of programming books, I would not hesitate to use information from a book I own, unless it was expressly forbidden in the text. I paid money for it after all. Why should anyone, especially an author, expect you to spend money for some technical information you can't actually use? That seems silly to me and is against common sense.

That's a reason the risk is low.  It was published, the authors know it will be spread wide. However, the risk is not zero.

Someone still has the rights, just like poems and songs that are published cannot be freely used without permission, puzzles and code snippets also cannot freely be used without permission. The original creator or publisher may not come after you, but then again, they might.

I'm not sure I agree with the advice here.

If you just use the puzzle without giving credit, then the authors of the book have no way of knowing if you got it from them or another source.  By giving credit or by contacting the authors, you are opening yourself up to legal action by admitting that you got the puzzle from them.

Example: the composer John Cage is famous for his piece 4'33", which consists of 4 minutes and 33 seconds of silence.  Musician Mike Batt included a minute-long silent track on one of his albums, jokingly credited John Cage as a co-composer, was sued by the John Cage Trust for using 4'33" without permission, and ended up paying a six-figure sum to settle the lawsuit.  Had he not given credit to John Cage, he probably wouldn't have been sued at all.  After all, John Cage does not own the concept of silence.

10 hours ago, a light breeze said:

By giving credit or by contacting the authors, you are opening yourself up to legal action by admitting that you got the puzzle from them.

Damned if you do, damned if you don't.

Hence the recommendation to talk to a lawyer to understand the risks for a specific situation.