Question:-
There are 100 Golfers in the local match play contest. If a player loses a match, he is immediately eliminated from the contest. How many matches will be played to determine the winner?
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Answer:-
If there is to be only one winner, than there are 99 loses, therefore, there were 99 matches. You can also do this with math: in round 1 there would be 50 matches to produce 50 winners, round 2 would have 25 matches to produce 25 winners, round 3 would have 12 matches to produce 12 winners ( one person of the 25 winners would have to wait until later to play again ), round 4 would have 6 matches to produce 6 winners, round 5 would have 3 matches to produce 3 winners, round 6 would have 2 matches ( the player left out before would now play to make it an even field ) to produce 2 winners, these 2 would play for the championship. So: 50+25+12+6+3+2+1=99
Alternate Answer:
The first round is 50 matches eliminating 50 golfers, the second is 25 matches eliminating 25 golfers. For the third round the remaining 25 are divided into pools of 5 at random and face two matches each (each vs. a different randomly selected opponent in the pool). I think you will find that there will be two golfers and two only from each pool who will be dual winners. They will advance. The third round was then 5 pools of 5 matches so 25 more matches (100 total so far). The fourth round will be 5 matches eliminating 5 golfers. These five participate in a pool (fifth round) just like the third round (5 more matches and 2 emerge). The two play the championship match. So by round the matches are: 50+25+25+5+5+1 = 111 matches