2. A chess tournament was attended by 5 players, and each played one game against each other. A player received 1 point for a win, half a point for a draw, and no points for a loss. The ranking of the players in the tournament was determined by the number of points scored. The only additional criterion for deciding the final placement of the players in case of a tie in points was the number of wins (the one with more wins is better placed). In the tournament, all players scored the same number of points. Vojta defeated Petr and shared first place with Tomáš. What was the result of the game between Petr and Martin?
2. Each player played one game against the remaining four. Therefore, a total of $\frac{1}{2} \cdot 5 \cdot 4=10$ games were played, so each player earned exactly 2 points. There are only three ways to earn 2 points by playing four games, and according to this, the overall table contained at most three equal groups of players. These groups, A, B, and C, are listed in the order in which they would be placed in the final table:

Group A includes all players who have two wins and two losses. Group B consists of players with one win, one loss, and two draws. Group C includes players with four draws.

Vojta and Tomáš are the only winners, so they do not belong to Group C. They also do not belong to Group B, because all three players in Group C, with a worse result, would have to draw with them (and each player in Group B has only two draws).

From this, it follows that Vojta and Tomáš have two wins and two losses, and Group C is empty. The remaining three players thus have one win, one loss, and two draws, which they must have played among themselves.

Conclusion. Petr and Martin drew with each other.

Alternative solution. We use the (redundant) information that Vojta defeated Petr: If Vojta and Tomáš had one win, one loss, and two draws, Petr would also have to be among the tournament winners. The only lower overall result is four draws, but Petr lost one game, so he must have won one. Therefore, Vojta and Tomáš have two wins and two losses. If Petr lost to Vojta, he must have defeated Tomáš. (He could not have two losses, as he was ranked lower than Tomáš and Vojta. Nor could he have drawn with Tomáš, who has no draws.) The necessary second point was earned by two draws - with Martin and the unnamed fifth player.

Conclusion. Petr and Martin drew with each other.

For a complete solution, award 6 points.