The authors learned a lot of mathematics from the problems encountered in various Romanian national contests. This is something that stayed with them for the entire of their careers. One of the goals of the book is to make the exposition of the material more interesting, at least for the beginners in Olympiad mathematics. Here and there they left unanswered questions related to the problems presented in the hopes that the reader will accept and even enjoy these challenges. The problems in the book were selected from the 1975 to 1986 Romanian Team Selection Tests. The problems are not only accompanied by their solutions, but also many have more than one solution and comments in order to make them clearer or to get connections to other problems.