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): \begin{center} \begin{tabular}{|c|c|c|c|} \hline Round & Match 1 & Match 2 & Match 3
\hline 1 & 1 vs 6 & 2 vs 5 & 3 vs 4
\hline 2 & 1 vs 5 & 6 vs 4 & 2 vs 3
\hline 3 & 1 vs 4 & 5 vs 3 & 6 vs 2
\hline 4 & 1 vs 3 & 4 vs 2 & 5 vs 6
\hline 5 & 1 vs 2 & 3 vs 6 & 4 vs 5
\hline \end{tabular} \end{center}
Explanation:
One team remains fixed.
Other teams rotate cyclically each round.
Ensures all teams play each other once.