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

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 $2^{2}=4$ 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.