6.16 The tennis association assigns numbers to tennis players based on their skill levels: the strongest player is ranked No. 1, the next is No. 2, and so on. Suppose that when two players whose number difference is greater than 2 compete, the player with the smaller number always wins. Now, the 1024 strongest players are participating in a singles tournament. The tournament is conducted on an elimination basis: participants are divided into pairs according to the draw results, and the two players in each pair play one match, with the winner advancing to the next round. Thus, after each round of matches, the number of players is halved, and after 10 rounds of matches, a champion is produced. What is the maximum possible number of the champion?
［Solution］Since athlete numbered $k$ can only lose to athletes with numbers not exceeding $k+2$, after each round of matches, the smallest number among the winning athletes can increase by at most 2. Therefore, after 10 rounds of matches, the number of the strongest athlete is at most 21.

Below, we point out that the 21st athlete cannot become the champion. If not, then after the first round, the 1st and 2nd athletes should be eliminated, but they can only lose to the 3rd and 4th athletes, respectively; after the second round, the 3rd and 4th athletes should be eliminated, but they can only lose to the 5th and 6th athletes, respectively; continuing this, after the 9th round, only the 19th and 20th athletes remain and compete in the final in the 10th round. Clearly, the champion cannot be the 21st athlete.

Finally, we provide an example where the 20th athlete becomes the champion. Divide all athletes into two groups: the first group consists of the 20th athlete and athletes numbered 514 to 1024, totaling 512 people, and the other 512 people form the second group. The first 9 rounds of matches are all played within the groups. Clearly, after 9 rounds, the only remaining athlete in the first group is the 20th athlete. The matches in the second group can be designed as follows: in the first round, the 3rd and 4th athletes defeat the 1st and 2nd athletes, respectively; in the second round, the 5th and 6th athletes defeat the 3rd and 4th athletes, respectively; ..., in the 8th round, the 17th and 18th athletes defeat the 15th and 16th athletes, respectively; in the 9th round, the 18th athlete defeats the 17th athlete. In the final 10th round, the 20th athlete defeats the 18th athlete.
In summary, the maximum possible number of the champion is 20.