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Difference between revisions of "2006 Romanian NMO Problems/Grade 9/Problem 4"
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==See also==
 
==See also==
 
*[[2006 Romanian NMO Problems]]
 
*[[2006 Romanian NMO Problems]]
 +
[[Category: Olympiad Combinatorics Problems]]

Revision as of 09:15, 28 July 2006

Problem

$\displaystyle 2n$ students $\displaystyle (n \geq 5)$ participated at table tennis contest, which took $\displaystyle 4$ 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 $\displaystyle 3$ students on the second place;
  • no student lost all $\displaystyle 4$ matches.

How many students won only a single match and how many won exactly $\displaystyle 2$ matches? (In the above conditions)

Solution

See also

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