2006 Romanian NMO Problems/Grade 9/Problem 4
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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;
- no student lost all matches.
How many students won only a single match and how many won exactly 
matches? (In the above conditions)
Solution
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