Difference between revisions of "2006 Romanian NMO Problems/Grade 9/Problem 4"
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How many students won only a single match and how many won exactly <math>\displaystyle 2</math> matches? (In the above conditions) | How many students won only a single match and how many won exactly <math>\displaystyle 2</math> matches? (In the above conditions) | ||
==Solution== | ==Solution== | ||
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==See also== | ==See also== | ||
*[[2006 Romanian NMO Problems]] | *[[2006 Romanian NMO Problems]] | ||
[[Category: Olympiad Combinatorics Problems]] | [[Category: Olympiad Combinatorics Problems]] | ||
Revision as of 10:49, 10 October 2007
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)
Solution
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