Difference between revisions of "2006 Romanian NMO Problems/Grade 9/Problem 4"
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==Problem== | ==Problem== | ||
| − | <math>\displaystyle 2n</math> students <math>\displaystyle (n \geq 5)</math> participated at table tennis contest, which took <math>\displaystyle 4</math> days. | + | <math>\displaystyle 2n</math> students <math>\displaystyle (n \geq 5)</math> participated at table tennis contest, which took <math>\displaystyle 4</math> days. Every day, every student played a match. (It is possible that the same pair meets two or more times, in different days). Prove that it is possible that the contest ends like this: |
* there is only one winner; | * there is only one winner; | ||
Revision as of 23:51, 5 November 2006
Problem
students 
participated at table tennis contest, which took 
days. Every day, every student played a match. (It is possible that the same pair meets two or more times, in different days). Prove that it is possible that the contest ends like this:
- there is only one winner;
- there are
students on the second place;
students on the second place;- no student lost all
matches.
How many students won only a single match and how many won exactly 
matches? (In the above conditions)
