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This paper deals with some issues related to the training of students of junior courses (approximately 14–19 years). At least two objectives are set. Firstly, we focus on potential participants of the programming Olympiads: according to our calculations, at least one third of the tasks of high-level Olympiads can be called exhaustive-searched. Secondly (which, apparently, is more important), mastering the proposed approach to the implementation of hard exhaustive-searched problems can (and should) serve as an “advanced” student as a first step into the “big science”: the tasks themselves, and the approach we propose to implement them, are closely connected with the set of directions of modern artificial intelligence, the analysis of large data, and similar subject areas. Several of the problems we are considering are related to different subjects. Among these problems (subjects areas) are, first, the tasks previously given at different levels of the ACM Olympiads, including at the final stage of this Olympiad. The solutions we offer for these tasks are no more complicated than the original ones, and considering that they can be quickly implemented using the approach we proposed (described in this article), we can say that they are much easier to learn by the trainees. In the article, we describe some classes implemented in C++, intended for the quick generation of programs for solving a variety of enumeration tasks. We give also some specific programming techniques for such tasks.