16 teams enter a competition

Question

16 teams enter a competition. They are divided into four pools (A, B, C and D) of four teams each. Every team plays one match against the other teams in its pool.

After the pool matches are completed:

• the winner of pool A plays the 2nd placed team of pool B.
• the winner of pool B plays the 2nd placed team of pool A.
• the winner of pool C plays the 2nd placed team of pool D.
• the winner of pool D plays the 2nd placed team of pool C.

The winners of these 4 matches then can play semi-finals, and the winner of the semi-finals play in the finals.

How many matches are played altogether?

Answer 1

4 teams per group (A, B, C and D), for every group, total number of matches are as follows:

assume that the teams in group A are 1, 2, 3, 4.

the matches for this group will be:

• 1 vs 2
• 1 vs 3
• 1 vs 4
• 2 vs 3
• 2 vs 4
• 3 vs 4

total = 6 matches, for each 4 groups 6*4 = 24 matches

then quarter finals, 4 matches

semi-finals, 2 matches

and finals 1 match.

total of 24 + 4 + 2 + 1 = 31 matches.

Answer 2

$4\cdot C(4,2)+7=31$.

Here $C(4,2)$ is like hand shake and after then there are $8$ teams and $7$ losers. (one loser in one game).