The purpose of an Opponent is to prove the contrary, i.e., to find errors in the solution presented. At the very beginning of the MathBattle, the Jury asks both teams if they want to challenge first. In case of a conflict, a Captain Contest is carried out. Only the Captains participate in this contest. The Captain who wins has a right to decide.
Teams take turns in challenging.
A the next time. Team A chooses an Opponent. Then the Opponent can ask the Speaker some questions which the Speaker answers. After the presentations, the Jury splits the score for the problem between the two teams. The Jury grades not only the solution but also the level of the Speaker's presentation of the solution and the level of the Opponent's commentary.