Example 8. In a Go tournament, ten players participate. Each player competes against the other nine players once. All players have different scores. The first and second place players have never lost a game, and the total score of the first two players is 10 points more than the second place player. The fourth place player's score is the same as the total score of the last four players. Please answer: How many points did each of the first to sixth place players get? (The winner gets 1 point per game, the loser gets 0 points, and in a draw, both get 0.5 points)
Let the scores of the ten selected players be $x_{1}, x_{2}, \cdots, x_{10}$.
(1) Obviously, the result of the match between the first and second place is a draw. Thus, $x_{1} \leqslant 8.5, x_{2} \leqslant 8$.
(2) The last four players have a total of 6 matches among themselves, so their total score $x_{1} + x_{8} + x_{9} + x_{10} \geqslant 6$.
(3) Since the score of the fourth place is equal to the total score of the last four players, $x_{4} \geqslant 6$, thus $x_{3} \geqslant 6.5$.
(4) If $x_{3} \geqslant 7$, then $x_{1} + x_{2} = x_{3} + 10 \geqslant 17$, which contradicts the result in (1), so $x_{3} < 7$, hence $x_{3} = 6.5$.
(5) Therefore, $x_{4} = 6, x_{1} + x_{2} = 16.5$, thus $x_{1} = 8.5, x_{2} = 8$.
(6) All ten players participate in a total of 45 matches, scoring 45 points, so the total score of the last six players is $45 - (8.5 + 8 - 6.5 + 6) = 16$ points, and the total score of the last four players is 6 points, thus $x_{5} + x_{6} = 10$, hence $x_{5} = 5.5, x_{6} = 4.5$.

In summary, the scores of the top six players are 8.5 points, 8 points, 6.5 points, 6 points, 5.5 points, and 4.5 points, respectively.