Annales du baccalauréat - Session 2021 - DNL mathématiques-anglais avec mention « section européenne »
Round Robin Tournament is a well-known type of tournament format that sport schedulers use.
Let $N$ be an even number of teams in the tournament. At the end of a Round Robin Tournament every team should have played against every other team. This method assumes that there are enough fields / pitches / courts so that all the games in a round can be played simultaneously. The technique is called the polygon method. There will be $N-1$ rounds (each team will play $N-1$ games). Since each team will play every other team once, no team will be idle* during any of the rounds. Let us schedule a round-robin tournament for 8 teams numbered from $1$ to $8$.
- Draw a regular $(N-1)$ sided polygon (i.e. a heptagon for 8 teams). Each vertex and the centre point represents one team.
- Draw horizontal stripes as shown. Then, join the vertex that has been left out to the centre. Each segment represents teams playing each other in the first round. So $(7, 6)$, $(1, 5)$, $(2, 4)$ and $(3, 8)$ play in the first round.
- Rotate the polygon $1/(N-1)$th of a circle (i.e. one vertex point). The new segments represent the pairings for round two.
- Continue rotating the polygon until it returns to its original position.
Extract from an article by Arunachalam Y. published on nrich.maths.org
- You are the organizer of a tournament with 6 teams, describe how many rounds you have and which team is playing versus which one in each round with the Round Robin method?
- If you had to organize a tournament with 5 teams, how would you organize it?
- scheduler: organisateur d’un planning
- idle: without work or activity
Version 1 (Laura Killian)
Version 2 (Jacob Chmielewski)
- pitch: terrain de sport
- vertex: sommet (plural: vertices)