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A total of 17 teams play in a single-elimination tournament. (A single-elimination tournament is one where once a team has lost, it is removed from the competition.) How many total games must be played before a winner can be declared, assuming there is no possibility of ties

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facundo3141592

By directly counting the number of games, we will see that there will be a total of 16 games.

How many games will be played?

Let's count the number of games, for each game, we need 2 teams.

Then with 17 teams, we can make 8 games (and one team will remain, they will pass directly to the next stage).

In these 8 games, 8 teams lose, then 8 teams are removed, this means that now we have:

17 - 8 = 9 teams left.

Now with these 9 teams, we can make 4 games (again, one team passes directly to the next stage).

In these 4 games, 4 teams are removed, then in the next stage we have:

9 - 4 = 5 teams left.

With 5 teams we can make 2 games, and after these 2 games, 2 teams are removed, so we have:

5 - 2 = 3 teams left.

With 3 teams we can make 1 game, and after that game 1 team is removed, then we have:

3 - 1 = 2 teams left.

With 2 teams we can make one, and the last, game.

Now adding all the numbers of games for each stage we have:

8 + 4 + 2 + 1 + 1 = 16

There are a total of 16 games.

If you want to learn more about counting, you can read:

https://brainly.com/question/251701

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