Question
There are 256 players in a chess tournament (singles). Two players play a match. Matches are played on a knockout basis, the loser is eliminated after each match. How many matches need to be played to declare a winner? There is no draw.___
Answer:
:
For two players, we need one match. The first round, having 256 players will need 2562= 128 matches.
Now there are 128 players left. To ensure that all players play a match, we need 1282= 64 matches
Continuing in the same way
Total number of matches = 128+64+ 32+ 16+8+4+2+1= 255
OR
In 1 match 1 player is eliminated
For tournament to conclude there should be only 1 winner and hence 255 players need to lose.
Hence we need 255 matches to eliminate 255 players.
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:
For two players, we need one match. The first round, having 256 players will need 2562= 128 matches.
Now there are 128 players left. To ensure that all players play a match, we need 1282= 64 matches
Continuing in the same way
Total number of matches = 128+64+ 32+ 16+8+4+2+1= 255
OR
In 1 match 1 player is eliminated
For tournament to conclude there should be only 1 winner and hence 255 players need to lose.
Hence we need 255 matches to eliminate 255 players.
Was this answer helpful ?
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