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Every year in my neighborhood we organize a basketball competition called “8 hours of basketball”. In order to have as many participants as possible, we reduce the games to 20 minutes in time (without stopping the clock), plus 10 minutes of preparation between matches.

Our competition model consists of games by lottery (looking for rest, if possible, the ones that have more matches at that time and that meetings between the same teams are not repeated as much as possible). The team that accumulates two defeats is eliminated, entering the classification according to the number of victories. In the end there must be a single champion, who will be the only one who has not lost two games in the entire tournament.

How many teams can we invite to play in these conditions?

#### Solution

Each eliminated team needs to lose two games to fall and the only surviving team may have lost a match at most. Thus, at the end of the tournament, if we count the amount of losses there will only be twice as many defeats (at most one more) than participating teams.

Since eight hours only allow us to play 16 30-minute games, The maximum number of teams that can participate is 7, ensuring that in a maximum of 15 games everything will be resolved.