Task 2 - 270832 In a chess tournament, each of the eight participants played exactly one game against each of the others; the points achieved by the individual players were all different. Bernd, who came in second place, scored as many points as the four last-placed players combined. Gerd came in third, and Uwe placed seventh.

Investigate whether it follows uniquely from these conditions what the result of the game between Gerd and Uwe was! If this is the case, then give the result!

Hint: In chess, a player receives 1 point for a win, half a point for a draw, and 0 points for a loss.
From the conditions, it follows that Bernd can have scored at most 6 points; for either the tournament winner won all seven of his games, including the one against Bernd, who came in second, or the winner scored at most 6 points, and Bernd, as the runner-up with a different point total, scored at most 6 points for this reason.

Therefore, according to the conditions, the four last-placed players together have also scored at most 6 points. However, they have already played 6 games among themselves and must have already earned a total of 6 points in these games.

Thus, they must have lost all their games against the top four. In particular, the seventh-place player lost to the third-place player; i.e., it follows unequivocally that Gerd won his game against Uwe.