A single-elimination tournament, also known as a knockout tournament, is one where the loser of a match is automatically eliminated from the tournament. The winners of each round continue to play each other until a single winner is declared. Determine the total number of matches that are necessary for a chess tournament involving 1024 participants.

Guest Feb 28, 2021

#3**0 **

*A single-elimination tournament, also known as a knockout tournament, is one where the loser of a match is automatically eliminated from the tournament. The winners of each round continue to play each other until a single winner is declared. Determine the total number of matches that are necessary for a chess tournament involving 1024 participants.*

After 1 round there are 512 participants.

After 2 rounds there are 256 participants.

After 3 rounds there are 128 participants.

After 4 rounds there are 64 participants.

After 5 rounds there are 32 participants.

After 6 rounds there are 16 participants.

After 7 rounds there are 8 participants.

After 8 rounds there are 4 participants.

After 9 rounds there are 2 participants.

After the **10**th round, there is one winner.

_{.}

Guest Feb 28, 2021

#4**+1 **

First round Start 1024 people

512 games 512 people left

256 games 256 people left

128 games 128 people left

64 games 64 people left

32 games 32 people left

16 games 16 people left

8 games 8 people left

4 games 4 people left

2 games 2 people left

only one game left----- last game for a winner ! A total of 1023 games played

ElectricPavlov Feb 28, 2021