2006 Romanian NMO Problems/Grade 9/Problem 4

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)

Page

Toolbox

Search

2006 Romanian NMO Problems/Grade 9/Problem 4

Problem

Solution

See also