O princípio da casa dos pombos e o princípio da invariância em problemas olímpicos

Abstract

The present study had the general purpose of studying the Principle of the Casa dos Pombos (PCP) and the Principle of Invariance (PI) applied to Olympic problems, culminating in yet another support and training material for students who are preparing for the Olympics. For this purpose, a descriptive research was used. The research was structured in four chapters, in the first there is a brief historical context of the National and International Mathematical Olympiad; The second chapter presents the theory that involves the pigeon house principle, necessary demonstrations and applications in Olympic problems with very detailed resolutions; The third chapter is similar to the second, but using the principle of invariance, demonstration and Olympic problems involving the content and the fourth chapter was devoted to problems as support in the studies of readers, it deals with the applicability of both the PCP and the PI. In it, tips of solutions are presented in order to mitigate any difficulties the reader may have with the topics covered in this material. The problems of the Casa dos Pombos Principle and Invariance Principle require, in order to solve them, not only combinatorial reasoning, but creativity and, above all, knowledge of other areas of Mathematics, because as both tools do not have formulas to be used in the resolution of problems, they demand from those who look at the subject to learn to work in a combined way these principles plus arithmetic, algebraic, geometric arguments, etc. The Olympic problems worked throughout this research allowed a wide range of situations in which this knowledge can be used, thus improving the logical-mathematical reasoning, mainly because they are classic questions, with simple, clear and understandable resolutions, which facilitate student understanding.