The present work should help considerably the students to their maths examinations, either for the mathematical competitions as well as in SAT math Level 2 exams. We apply, in a very simple and instructive way, knowledge from Cognitive Psychology (see: How the mind works, 1980) which is the easiest and fastest way to learn and remember. This book consists of two parts: In the first part we present answers to the two questions: Is there any technique that can help someone who is thoroughly stuck with a problem and no idea seems to come in mind? - Is there any technique that can help someone who is trapped into a loop and makes circles around the problem, since the solution lies elsewhere? In the first part we present easy and efficient techniques which improve our ability to overcome the above difficulties. The techniques have been tested many times at the Experimental School of the University of Athens , where the first of the authors was the director. They helped students to become better problem solvers There are also many examples where we apply the techniques so that they will be completely clarified. The first part is written by Dr. Spyros Kalomitsines. The other part is written by Dr. Spyros Kalomitsines and Dr. Fotios I. Travlopanos.