# Question for a wet weekend.

Discussion in 'Math' started by studiot, Apr 19, 2008.

1. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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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!

2. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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Is N even or odd?

John

Edit: Just 0ne (1)

3. ### Caveman Active Member

Apr 15, 2008
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Actually it's nice and sunny here.
In single elimination each match removes one person, so N-1.

4. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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I respectfully disagree, Caveman. As worded, all of the other matches determine who will not win. Only one match determines who wins. John

5. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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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.

6. ### jpanhalt AAC Fanatic!

Jan 18, 2008
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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

7. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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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.

8. ### Caveman Active Member

Apr 15, 2008
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Actually, since you cannot play that final match without playing the others, all matches must be played.

9. ### Caveman Active Member

Apr 15, 2008
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The obvious question is whether it is single elimination.

10. ### jpanhalt AAC Fanatic!

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

11. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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It's not meant to be a trick question like the St Ives one or spell IT.

12. ### Wendy Moderator

Mar 24, 2008
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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.

13. ### Caveman Active Member

Apr 15, 2008
471
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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.

14. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
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Hi Caveman - have a dino steak to celebrate

Meet the Flintstones.

15. ### drewlas New Member

May 12, 2008
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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