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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.

 Feb 28, 2021
 #1
avatar+48 
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What happens if there is an odd number of ppl?

 Feb 28, 2021
 #2
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The tournament organizers deliberately arrange it so that there are 1024 deci-finalists.  Is that a word?  It is now. 

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Guest Feb 28, 2021
 #3
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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 10th round, there is one winner. 

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 Feb 28, 2021
 #4
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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

 Feb 28, 2021

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