Técnicas (não) usuais de resolução de problemas: paridade, argumentos combinatórios, contagens duplas, invariância e colorimentos

Abstract

The aim of this work is to address techniques for solving unusual problems in various contexts, exploring their application in combinatorial arguments and double counting for elementary school students. By examining different situations, methods of counting involving invariants are highlighted, providing a deeper understanding of the underlying mathematical properties. Additionally, the analysis covers the theory of graph coloring, emphasizing the importance of combinatorial techniques in solving problems related to graph coloring. The interconnection between parity, combinatorial arguments, double counting, invariants, and coloring is explored to demonstrate the applicability of these concepts in a variety of mathematical situations, revealing the intrinsic relationships between these areas.