Mathematics has a lot of beauty in it, however, many students do not discover it. While mathematics textbooks are gradually becoming more full of illustrations, the nonstandard math problem books, especially for older students, usually have very simple design. There is a special lack of attractive math puzzle books for 12–15 years old junior youth. The article explores what attributes and design should a math puzzle book for this age group have in order that it would, on one side, be attractive, interesting and close to them, and, on the other, would help to independently gradually develop their capacities of logical thinking. To respond to that, various literature is analyzed, a survey is carried out, and a project of such a book presented.