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Question for a wet weekend.

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studiot

Thread Starter

studiot

Joined Nov 9, 2007
4,998
There are N entrants to a knockout tennis tournament. Assuming all matches produce a result how many matches must actually be played to decide the winner?

When you have guessed for small N, provide a better answer than guessing!
 
studiot

Thread Starter

studiot

Joined Nov 9, 2007
4,998
You guys may be interested to know that both this question and the Fly question were Oxford University entrance (interview) questions for maths in the 1960s.
 
J

jpanhalt

Joined Jan 18, 2008
11,087
So, what's the expected answer?

I don't think we know enough about N (e.g., odd, even; power of 2 or not) to answer the question any other way. Perhaps, I don't understand the format of a "knockout" tournament. Is it like the Wimbledon tournament?

If Oxford rejected me on that basis in 1960, I would have gone to Harvard, MIT, Caltech, or maybe even Princeton. John
 
studiot

Thread Starter

studiot

Joined Nov 9, 2007
4,998
N is any integer greater than zero.

In a knockout tournament contestants are paired for matches. Odd contestants get byes so do not actually play in some rounds.

Hope this helps, but it's too early to referee the answer.
 
J

jpanhalt

Joined Jan 18, 2008
11,087
It depends on how you read the question. Counting the qualifying matches, and assuming single elimination, I agree with you. John
 
Wendy

Wendy

Joined Mar 24, 2008
23,797
Pick the base 2 number above the number of contestents (1,2,4,8...) and count levels. I could express this a lot better, but it's been a long day. 5 - 8 contestants would be 4 games.
 
C

Caveman

Joined Apr 15, 2008
471
Its not that hard. It doesn't ask number of levels, but rather how many matches must be played. Since every match eliminates one person, unpaired people get byes, and you must get down to one remaining, it is = (the number of contestants) - 1.
 
D

drewlas

Joined May 12, 2008
7
In a tournament with N players, N-1 players lose one match and each match is lost only once. So if there are N players then the number of matches is N-1.
drewlas
 
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