# A Tennis championship is played on knockout basis i.e. a player is out of the tournament when he loses a match how many players particpated the tournament if 31 matches are totally played

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by 1Rahulanand

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by 1Rahulanand

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If n players play:

At the first level there are n/2 matches, next level n/4 matches, next level n/8. and so on until there is just one match.

matches = 1+ 2+ ..+ n/4 + n/2 => initially there are n players in the tournment. After first round of n/2 matches there are n/2 players to play next round. In the next round n/4 players.

Number of matches total 31 = 1+ 2 + 4 + 8 + 16 = 1 + 2 + 2^2 + 2^3 + 2^4

Initial first round there were 2^4 = 16 matches=> 32 players were there.

At the first level there are n/2 matches, next level n/4 matches, next level n/8. and so on until there is just one match.

matches = 1+ 2+ ..+ n/4 + n/2 => initially there are n players in the tournment. After first round of n/2 matches there are n/2 players to play next round. In the next round n/4 players.

Number of matches total 31 = 1+ 2 + 4 + 8 + 16 = 1 + 2 + 2^2 + 2^3 + 2^4

Initial first round there were 2^4 = 16 matches=> 32 players were there.