The collection prepared by N. Vasiliev and A. Yegorov contains tasks that do not require any special knowledge that goes beyond the secondary school program, but require a certain independence of thought and ingenuity. At the end of the collection are examples of problems proposed at the All-Russian Mathematical Olympiads. In 1963, it is planned for the best participants of the All-Russian Olympiad who graduated from the IX grade of 10: summer school or the X grade of an 11-year school, to organize in Moscow "summer mathematical school 1...