A book in detail tells about mathematical competitions on the summer tournaments of the name А. П. Савина. Complementing the previous books of authors, a book collected all tasks of tournaments 2015-2016, and also the best tasks of tournaments 1999-2001 years. Collection turned out more than from 450 tasks for students 6-9 classes. Tasks are grouped on themes, provided with рубрикатором, to all the decisions or pointing are given. Most tasks are fully accessible to the wide circle schoolchildren.At the end of book the article over, in that the questions of search on the rectangular boards of most number of cages are understood with different попарными distances between their centers, is brought. Also the tasks of competition of captains, that is conducted at the beginning of every fight, are accommodated in a separate head.A book is addressed to those, who would like to prepare or prepare students to the mathematical fights and other competitions : to the schoolchildren, them to the parents and teachers, and also simply to the mathematics lovers.