The article summarizes the experience of training masters of mathematics for organizing and conducting Mathematics Olympiads for schoolchildren. The purpose of the article is to characterize and summarize the methodological features of the training masters of mathematics for the organization of Mathematics Olympiads for schoolchildren. Among the research methods used, the following were decisive: analysis and generalization of scientific and methodical sources for the theoretical justification of the highlighted problem, modeling, and synthesis of the obtained data. Conclusions. Various possibilities of implementing such training have been analysed by the authors, taking into account the realities of the current state of the educational system of Ukraine. The methodical features of teaching master’s students in mathematics to solving and creating mathematics olympiad problems and discrete subjects for schoolchildren are considered in the article. The benefit of the article is that the numerous examples of the implementation of the «to solve a problem – to replicate problems» approach proposed by the authors are presented, and the methodological expediency of its use in the educational process is substantiated. Conclusions. The authors have singled out the promising directions for further research in this field: the creation of appropriate educational and methodological support for the implementation of the approach «learning to solve a problem - learning to replicate problems» within the framework of other content lines of the course «Mathematics Olympiads problems: creation and solution» in the training of masters in mathematics (logical, stochastic, cryptographic, etc.) at pedagogical higher education institutions; the implementation of elements of this approach to the system of practicing teachers professional development the acquaintance high school students who study mathematics in depth with the relevant methods. The indisputable interest is in the creation of masters’ practice-oriented developments, as the part of their educational and research work, aimed at other aspects of the school mathematics education fundamentalization

methodical training of masters of mathematics, Mathematical Olympiads for schoolchildren, problem solving, replication of problems, arithmetic, graph theory