Nowadays, in the time when the level of teaching universally decreases and “pure” science does not appeal as it used to, this book can attract new students to mathematics.
The book can be useful to all teachers and instructors heading optional courses and mathematical groups. It might interest university students or even scientists. But it was primarily intended for high school students who like mathematics (even for those who, perhaps, are unaware of it yet) and to their teachers. The complete answers to all problems will facilitate the latter to coach the former.
The book also contains some history of Moscow Mathematical Olympiads and reflections on mathematical olympiads and mathematical education in the Soviet Union (the experience that might be of help to western teachers and students). A relation of some of the problems to “serious” mathematics is mentioned.
The book contains more than all the problems with complete solutions of Moscow Mathematical Olympiads starting from their beginning: some problems are solved under more general assumptions than planned during the Olympiad; there extensions are sometimes indicated. Besides, there are added about a hundred selected problems of mathematical circles (also with solutions) used for coaching before Olympiads.
The Moscow Mathematical Olympiad was less known outside Russia than the “All-Union” (i.e., National, the USSR), or the International Olympiad but the problems it offers are on the whole rather more difficult and, therefore, it was more prestigious to win at. In Russia, where sports and mathematics are taken seriously, more than 1,000,000 copies of an abridged version of a part of this book has been sold in one year.
This is the first book which contains complete solutions to all these problems (unless a hint is ample, in which case it is dutifully given)
