Twenty four teams are divided into 4 group of six teams each. Within each group the teams play each other exactly once. The winners of each group then play in the semifinals. Winners of the semifinals play in the finals and losers for the 3^rd place. How many matches are played?

Solution

Step 1: Group Stage Matches

In each group of 6 teams, every team plays every other team exactly once (round-robin format).

Formula: Number of matches in a group = ⁿC₂ = n!/(2!(n-2)!)

Where n = 6 teams

Matches per group = ⁶C₂ = (6 × 5)/(2 × 1) = 15 matches

Total groups = 4

Group stage total = 15 × 4 = 60 matches

Step 2: Semifinal Matches

The 4 group winners advance to the semifinals.

Two semifinal matches are played.

Semifinals = 2 matches

Step 3: Final Stage Matches

After semifinals, two matches determine final rankings:

• Final match (1st vs 2nd place) = 1 match
• 3rd place playoff (semifinal losers) = 1 match

Final stage total = 2 matches

Step 4: Total Matches

Total matches = Group stage + Semifinals + Finals

Total matches = 60 + 2 + 2 = 62 matches