7. (10 points) There are 16 players participating in a chess promotion tournament, where each pair of players competes in one match. The winner of each match gets 1 point, the loser gets 0 points. If it's a draw, each player gets 0.5 points. After all the matches are completed, players with at least 10 points advance. How many players can advance at most in this tournament? $\qquad$
【Analysis】16 participants will have a total of $(1+15) \times 15 \div 2=120$ matches, and regardless of victory or defeat, each match totals 1 point, so the total score of the matches is 120 points. The most ideal outcome would be $120 \div 10=12$ people advancing, meaning 12 people, each with 10 points, and the remaining 4 people with 0 points each. However, this situation is impossible (even the last two ranked participants will score points in their match against each other). Therefore, consider the case of 11 people. The top 11 are called experts, and the bottom 5 are called amateurs. The experts draw all their matches against each other, each scoring $0.5 \times 10=5$ points. The experts win all their matches against the amateurs, each earning an additional 5 points. This way, each expert scores 10 points, qualifying them all to advance.

【Solution】16 participants will have a total of $(1+15) \times 15 \div 2=120$ matches, and regardless of victory or defeat, each match totals 1 point, so the total score of the matches is 120 points. The most ideal outcome would be $120 \div 10=12$ people advancing, meaning 12 people, each with 10 points, and the remaining 4 people with 0 points each. However, this situation is impossible (even the last two ranked participants will score points in their match against each other). Therefore, consider the case of 11 people. The top 11 are called experts, and the bottom 5 are called amateurs. The experts draw all their matches against each other, each scoring $0.5 \times 10=5$ points. The experts win all their matches against the amateurs, each earning an additional 5 points. This way, each expert scores 10 points, qualifying them all to advance. In summary: a maximum of 11 people can advance;
Therefore, the answer is: 11.