There are many important issues in informatics and many agree that algorithms and programming are most important issues that need to be included in informatics education (Dagiene and Jevsikova, 2012). In this paper, we propose how some of these issues can be easily taught using the notion of a formal system which consists of axioms and inference rules by which theorems can be proved. As is argued in (Dagiene and Jevsikova, 2012), we can introduce important topics in informatics using puzzle-like examples and students do not need to have prerequisites for learning. The materials presented in this paper have been used in a college-level elective class titled Hypertext and Computability in our university since the fall semester of 2008 and we believe that the contents proposed in this paper can be easily used to teach beginner students without technical backgrounds.