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Two teams from Russia have been participating in IMMC every year since its first edition. Initially, only two schools were involved in the selection, but step by step, the number of schools and teams increased, and lately we have about 30 teams from the places scattered all over the country, from Siberia through Urals to Caucasus and to Moscow, competing for a pass to the international round. To popularize IMMC and related activities, we use various events for high school students and teachers, most notably, the international Mathematical Modeling Tournament (MMT) conducted annually by the Kolmogorov School of MSU. MMT comprises four contests, one of which is similar to IMMC and the other three are closer to traditional olympiads in terms of their format and to applied mathematics in terms of content, which makes them easier accessible for unprepared students. Sample problems from MMT will be presented. More generally, we will discuss the reasons why Russian teams are not as successful at IMMC as could be expected judging by their results at IMO and other traditional olympiads.