2006 Romanian NMO Problems/Grade 9/Problem 4
Problem
students 
participated at table tennis contest, which took 
days. In every day, every student played a match. (It is possible that the same pair meets twice 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)
