Question 178
A country held a one-round tennis tournament. Participants received $1$ point for winning the match, and $0$ points for losing. There are no draws in tennis. At the end of the tournament, Oleksii saw the number of points scored by each participant, as well as the schedule of all the matches in the tournament, which showed the pairs of players, but not the winners. He chooses a match in some particular order (however he wants) and tries to guess the winner, after which he is told if he is correct. Prove that Oleksii can act in such a way that he is guaranteed to guess the winners of more than half of the matches.
(Oleksii Masalitin)
(Oleksii Masalitin)