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?

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 teams

We can write the following equation :

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

Therefore,

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.