Abstract
In this paper, we consider several ways to solve problems of high complexity that occur in the school course of mathematics, test tasks of mathematical literacy, and Olympic problems. Problem solving is the most productive form of learning mathematics, and this process should be a necessary component of all extracurricular activities conducted in mathematics. Mathematical Olympic problems, as a rule,will help to a large extent to learn, to find independent nonstandard methods of solving problems. The main goal of solving problems of high complexity plays a special role in the development of students. Helps them learn the material more strongly and consciously. The ability to analyze a given situation, compare data and search for data, determine the hidden properties of this case, synthesize useful information for solving problems, and form the necessary skills not only for solving problems. The high school program considered solving equations that are not defined using Euclid's rules for catching ordinary multipliers,classifying complex expressions by the properties of Prime numbers, and solving economic problems