Question 52
In an internet chess tournament 2005 chess players took part and everyone played one game against any other. After the tournament it appeared that for every two players $A$ and $B$ who had drawn their game every other player had lost his game with $A$ or with $B$. Prove that if there were at least two draws in the tournament then the players can be ordered in such a way that everyone has won his game with the next one in the sequence.
Emil Kolev
Emil Kolev