The mathematical carousel is a team competition. Each team has 6 or fewer players (in case of exclusion, the team may consist of more participants). 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. Participants who are at different boundaries should not communicate with each other. Therefore, usually the organizers of the carousel place the players of the initial boundary of this team in one place, and the players of the scoring boundary — in another, at some distance from the place of the initial boundary.

First, all team players (usually six people) are located at the starting line in a certain order — from participant #1 to participant #6. The order (numbering of participants) the team determines itself before starting the carousel. According to the signal of the beginning of the competition, each team is given the first task. When the command solved the problem, it writes on the back a piece of paper on which the problem was issued, the answer to it (only the answer is a complete solution and proof is not necessary). The paper team returns to the jury member who checks the answer. If the answer is wrong, nothing happens, the command just gets the next task. If the answer is correct, one of the team members — No. 1 — switches from the initial boundary to the scoring.

Next, the players at the starting and scoring boundaries work independently. And those and others are given new tasks every time. If the players of the initial turn provided the correct answer to the next task, one of them — the one who was the first in the queue — goes to the scoring line (and sits at the end of the scoring queue). If the players of the scoring boundary gave the wrong answer, the player who was the first in the scoring queue goes back to the starting line (and sits at the end of the initial turn). Thus, team players move between the starting and scoring boundaries in a way that resembles riding a carousel. If at the initial turn the task is given the wrong answer, or on the scoring – correct, all players remain in their places.