# 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

2
by 1Rahulanand

2014-07-31T13:16:35+05:30
Since there are two players per match, at first 32/2 = 16 matches will be held( half of them will be eliminated in knock out) 16winners would play 8 matches against each other. 8 winners would play 4 matches against each other and so on. To put together, the number of matches played will be 16+8+4+2+1 =31matches. This exactly matches the data in question. So my assumption is 32 players is correct.
2014-07-31T14:37:43+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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.