What is Reddit's opinion of The Art and Craft of Problem Solving?

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Art and Craft of Problem Solving by Zeitz

Just search amazon for Art of Problem Solving and you'll get a tonne of resources

You can also look at The Art and Craft of Problem Solving by Paul Zietz.

Also, do you understand why the correct answer is 1 in your question?

It sounds like you want olympiad books. Try https://www.amazon.com/Art-Craft-Problem-Solving/dp/0471789011/ref=sr_1_1?s=books&ie=UTF8&qid=1488413168&sr=1-1&keywords=art+and+craft+of+problem+solving to begin with, then look into something more advanced, like https://www.amazon.com/Mathematical-Olympiad-Challenges-Titu-Andreescu/dp/0817645284

I think this is what you are looking for.

Competitive math problems are the best way to improve pure math skills. Although quite different from what would be considered mathematical research, they build core problem solving intuition. Look into the following:

http://www.artofproblemsolving.com/ - Website and forum dedicated to pure and competitive math problems, as well as the skills needed to solve them. They also keep archives of past competition problems. I recommend that you start looking at the AMC and AIME competitions, and see if you can participate in the AMC before you graduate. It's offered in February for high schoolers.

http://209.222.159.179/amc/a-activities/a7-problems/putnamindex.shtml - Website to find past problems from the Putnam Competition, a collegiate undergraduate math competition. These are very difficult for someone who is just starting off but are still very good problems to look at. If you are planning on majoring in math then I recommend that you take the Putnam exam all 4 years.

http://www.usamts.org/ - Website for USAMTS, a high school mathematics competition sponsored by the NSA. USAMTS is a lot different from typical competitions in that instead of a strict time limit, the problems are put out a month before any solutions are due. They also provide resources on their site for those who are unfamiliar with proof writing. The first round has already finished and the second round is due in about 2 weeks. However, you can jump in at any time, and if you score nicely you can get a lot of free stuff. I recommend that you do this, even if you don't plan on submitting your solutions.

As for books, I recommend Paul Zeitz's Art and Craft of Problem solving:

http://www.amazon.com/Art-Craft-Problem-Solving/dp/0471789011

This is one of the best books to get acquainted with the mental process for solving difficult math problems, as well as some of the more advanced techniques which you probably didn't pick up if you are just starting to become interested in more difficult math problems. If you don't want to spend the money, I'm sure you can find it online somewhere, but it's worth every penny.

http://www.amazon.com/Art-Craft-Problem-Solving/dp/0471789011