### Brain Teasers

# 100 Golfers

There are 100 golfers in the local match play contest. Each match has only 2 players. If a player loses a match, he is immediately eliminated from the contest. How many matches will be played to determine the winner?

### Answer

If there is to be only one winner, then there are 99 losers, 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=99Hide Answer Show Answer

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## Comments

In any knock-out competition, there is one less game than the number of players i.e. 83 players, 82 games; 91 players, 90 games. Simple.

No one would ever run a tournament like that, allowing one player three consecutive byes. A different player should get a bye each time there's an odd number of players.

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