The mathematical carousel is a team competition. Each team has 6 or fewer players. Some of the team members are on the so-called starting line during the carousel, the rest of the team is on the scoring boundary. While the competition continues, some participants move from the initial boundary to the scoring, and sometimes vice versa.
A mathematical battle is a competition of two teams, which consists in solving problems, narratoring their own solutions and finding and exposing shortcomings in the solutions of opponents. First, the participating teams receive the conditions of battle tasks. The set of tasks is the same for both teams and is not known to them in advance. For some time, the teams independently solve problems, and then gather in a common audience and start, in fact, the battle.
Team Blitz is a short competition held to determine in the event of a draw, but more than 2 teams can compete here at equal figures. Such situations occur when 3 or more teams score the same number of points in the previous group tournament. And for face-to-face meetings, each team must take its place.
Mathematical abaka is a team game-competition for solving problems. All tasks are issued to solve all commands at once. The main scoring indicator in mathematical abstraction is the total number of points scored (including bonuses). In the case of equality of points for several teams, a higher place is taken by a team that has a larger amount of bonuses. With equality and this indicator, teams are considered to share seats.
Mathematical Zanzibar is a team competition. Each team has 6 or fewer players (in case of exclusion, the team may consist of more participants). Before starting zanzibar, teams are given at once all the tasks (from 10 to 30), which they solve within 2 hours. The jury only checks the answer. If it is true, it is considered that the command solved this problem correctly, if the answer is not correct or complete, then the task is counted as unsealed.
Mathematical tennis is an individual competition in which any number of participants can participate, let them be N, which satisfies the condition – it is greater than or equal to 2^k , but less than 2^(k+1) (hereinafter we will consider N=75 as an example). At the beginning of the competition, a draw is held and each participant receives a number from 1 to N. The competition will last exactly k rounds.