In the paper problems which organizers of Olympiads are faced considered. The approach to solve this problems suggested. This approach is based on activity theory and includes using rather simple constructive problems as a first step to more complicated theoretical ones. The experience of implementing this approach within the framework of the Olympiad in Discrete Mathematics and Theoretical Informatics is described. The focus is set on computer manipulators -interactive dynamic models of mathematical and informatical object.

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Higher education in general and engineering education in particular are divided into three levels in Russia. The first level is the Bachelor’s degree course; the second level is the specialist and Master’s degree program; the third level is the postgraduate training program.