A basketball tournament starts with 64 teams. After one loss the team is out. How many games will the winning team play in the tournament?
Here's one way to find the answer.
With 64 teams:
Round 1: 32 games
Round 2: 16 games
Round 3: 8 games
Round 4: 4 games
Round 5: 2 games
Round 6: 1 game
In a basketball tournament with 64 teams where each team is eliminated after one loss, let's determine how many games the winning team will play.
Since one team is eliminated after each game, there will be 32 teams remaining after the first round. Then, 16 teams will be left after the second round, 8 teams after the third round, 4 teams after the fourth round, and 2 teams after the fifth round.
Finally, in the sixth round, the two remaining teams will compete in the championship game. The winning team will be the tournament champion.
To summarize:
Round 1: 64 teams
Round 2: 32 teams
Round 3: 16 teams
Round 4: 8 teams
Round 5: 4 teams
Round 6: 2 teams (Championship game)
Therefore, the winning team will play a total of 6 games in the tournament.
To determine the number of games the winning team will play in the tournament, we can analyze the structure of the tournament.
Given that each team is eliminated with one loss, this implies that there is a single-elimination setup, where teams are eliminated from the tournament after losing a game.
In a single-elimination tournament, the number of teams is reduced by half after each round. Therefore, to find the number of games played in the tournament, we need to find the number of rounds until a single team remains.
Starting with 64 teams, each round reduces the number of teams by half. So, the number of teams remaining after each round can be calculated as follows:
Round 1: 64 teams
Round 2: 32 teams
Round 3: 16 teams
Round 4: 8 teams
Round 5: 4 teams
Round 6: 2 teams
Round 7: 1 team (winner)
To find the number of games played, we need to sum up the number of games played in each round. In each round, half the number of teams will win and advance to the next round (while the other half is eliminated). Since each game has two teams, the number of games played in each round is equal to half the number of teams in that round.
Calculating the number of games played in each round:
Round 1: 64 teams / 2 = 32 games
Round 2: 32 teams / 2 = 16 games
Round 3: 16 teams / 2 = 8 games
Round 4: 8 teams / 2 = 4 games
Round 5: 4 teams / 2 = 2 games
Round 6: 2 teams / 2 = 1 game
Adding up the number of games played in each round gives us the total number of games played:
32 + 16 + 8 + 4 + 2 + 1 = 63
Therefore, the winning team will play a total of 63 games in the tournament.