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# Question for a wet weekend.

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

1. ### studiot Thread Starter AAC Fanatic!

Nov 9, 2007
5,003
523
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 Expert

Jan 18, 2008
7,683
1,889
Is N even or odd?

John

Edit: Just 0ne (1)

3. ### Caveman Senior Member

Apr 15, 2008
471
1
Actually it's nice and sunny here.
In single elimination each match removes one person, so N-1.

4. ### jpanhalt Expert

Jan 18, 2008
7,683
1,889
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
5,003
523
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 Expert

Jan 18, 2008
7,683
1,889

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
5,003
523
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 Senior Member

Apr 15, 2008
471
1
Actually, since you cannot play that final match without playing the others, all matches must be played.

9. ### Caveman Senior Member

Apr 15, 2008
471
1
The obvious question is whether it is single elimination.

10. ### jpanhalt Expert

Jan 18, 2008
7,683
1,889
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
5,003
523
It's not meant to be a trick question like the St Ives one or spell IT.

12. ### Wendy Moderator

Mar 24, 2008
21,839
3,051
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 Senior Member

Apr 15, 2008
471
1
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
5,003
523
Hi Caveman - have a dino steak to celebrate

Meet the Flintstones.

15. ### drewlas New Member

May 12, 2008
7
0
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