Contests and Olympiads should be considered not only as a way of comparing the students' levels of training. They can be regarded as a different way of organizing the mental activity of participants. Different types of tasks initiate various types of intellectual activity among students. The Olympiad tasks differ from "school" ones by non-standardness, a combination of the understandability of the formulation and the non-obviousness of the solution, the possibility of various approaches to solving the problem. At the same time, the variety of contests and Olympiads raises the task of investigating and classifying them, focusing on supporting different styles of thinking. In this paper, we carry out an analysis of contests and Olympiads in informatics, aiming at identifying aspects of the student's intellectual activity, which are not sufficiently evaluated at school. The Olympiad in Discrete Mathematics and Theorethical Informatics is at the intersection of the two sciences. The article deals with the problems encountered by the organizers of competitions in mathematics and computer science and demonstrates some ways to solve them using the example of the Olympiad.

Based on the technology of teachers' educational coaching, a methodical approach of interaction between students and teachers for solving a non-standard task by a student a task with "extra" data in the condition, is demonstrated. The presented methodology is designed to help students develop the necessary skills to successfully complete the task. The main stages of the methodology are detailed, from critical understanding of the task (topic), goal setting, motivation of activities and the choice of strategy to a creative approach to solving the task and analyzing the results. The role of the teacher consists in posing guiding questions, increasing student motivation, monitoring difficult situations while moving towards a set goal. The result is the unlocking of the child's potential for the formation of his inner desire to "learn how to learn". During the coaching session, the effectiveness of various graphical models was considered and evaluated using the example of solving a logical problem.