Question

The Alphaville Youth Basketball committee is planning a single-elimination tournament (for all the games at each round, the winning team advances and the losing team is eliminated). The committee wants the winner to play 4 games. How many teams should the committee invite?

Answer 1

The committee should invite 16 teams.

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
`2^(2)=4` teams

We can write the following equation :

`2^(a)=b`

Where a is the total victories that we want for the winner team and b is the total number of teams invited.

Therefore,

`2^(4)=16` 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.