Answer:
The committee should invite 16 teams.
Step-by-step explanation:
The committee wants the winner to play 4 games ⇒ The winner must achieve 4 victories.
Let's think this problem from end to beginning.
In the last game, the winner team plays against the finalist.
In the previously game, the winner team plays against a team A and the finalist team plays against a team B (a total of 4 teams)
Then, for 2 rounds we have [tex]2^{2}=4[/tex] teams
We can write the following equation :
[tex]2^{a}=b[/tex]
Where a is the total victories that we want for the winner team and b is the total number of teams invited.
Therefore,
[tex]2^{4}=16[/tex] will be the total number of teams invited if we want the winner team to achieve 4 consecutive victories.
This equation is valid when after a game the winning team advances and the losing team is eliminated.
