Question

Draw a league fixture for 6 teams using the Cyclic Method.

Hint:

For even teams: Rounds = \( n - 1 \). For odd teams: Add a dummy team and apply the cyclic method.

Answer 1

Concept: In a league tournament, each team plays every other team once. The cyclic method is used to generate fixtures by fixing one team and rotating the others in a circular pattern. 
Step 1: Number the Teams Let the teams be: \[ 1, 2, 3, 4, 5, 6 \] Total teams = 6 (even number) Number of rounds = \( n - 1 = 5 \) 
Step 2: Fix One Team Keep Team 1 fixed and rotate the remaining teams clockwise. 
League Fixture Table (Cyclic Method): 

Explanation: 
One team remains fixed. 
Other teams rotate cyclically each round. 
Ensures all teams play each other once. 
 

 

Answer 2

A league fixture for 6 teams can be built without a diagram by using the standard circle (cyclic) rotation rule, working purely from the numbers involved.

Setting up: Since there are 6 teams, an even number, every team plays 5 matches (one against each of the other teams), spread across 5 rounds, with 3 matches happening in parallel in each round.
The rotation rule: Picture the 6 teams as 6 seats, one fixed and five that rotate. Keep Team 1 anchored in its seat and, before each round, move every other team one seat further around the circle (in the same direction, say clockwise). Whichever two teams end up seated opposite each other in a round play that fixture.
Working it through: Starting with the natural order 1-2-3-4-5-6 opposite pairs read as 1v6, 2v5, 3v4 (Round 1). Rotating teams 2-6 by one seat gives 1v5, 6v4, 2v3 (Round 2). One more rotation gives 1v4, 5v3, 6v2 (Round 3), then 1v3, 4v2, 5v6 (Round 4), and finally 1v2, 3v6, 4v5 (Round 5).
Checking the result: Listing out each team's opponents across the five rounds confirms every team meets each of the other five exactly once, with no repeats and no team left without a match in any round.

This rotation-based working reaches the same fixture list that the cyclic method diagram represents: 5 rounds of 3 matches each, covering all 15 possible pairings among the 6 teams.