there are 150 members in my club. we decided to have a ping pong tournament. all the members came forward to play in the game. every time a member loses a game he is out of the tournament. there are no ties. can you tell how many games must be played in order to determine the champion?
there are 150 members in my club. we decided to have a ping pong tournament. all the members came forward to play in the game. every time a member loses a game he is out of the tournament. there are no ties. can you tell how many games must be played in order to determine the champion?
Answer: In a single-elimination ping pong tournament with 150 members, every time a member loses a game, they are out of the tournament. To determine the champion, there will be 149 games played.
Here’s the breakdown:
- In the first round, there are 150 participants, so 75 games will be played (as each game eliminates one player).
- In the second round, there will be 75 players remaining, resulting in 37 games (one player gets a bye since there’s an odd number).
- This process continues until there is only one player left, who becomes the champion.
So, the total number of games played to determine the champion is 75 + 37 + 18 + 9 + 5 + 3 + 1 = 149 games.