6.44 $A, B, C$ three countries are holding a Go team tournament, each team has 9 members. The rules are as follows: each match involves one player from each of the two teams, the winner stays to defend, the loser is eliminated, and the other team sends one player to challenge. The tournament starts with one player from each of $A$ and $B$ teams, and proceeds in this manner. If any team has all 9 members eliminated, the remaining two teams continue to compete until another team is completely eliminated. The winner of the last match's team is the champion. Answer the following questions and provide reasons:
(1) What is the minimum number of wins for the champion team?
(2) If the champion team wins 11 matches at the end of the tournament, what is the minimum number of matches that could have been played in the entire tournament?
[Solution] (1) Since teams $A$ and $B$ first compete against each other, and then the winner competes against team $C$, we only need to consider the scenario where team $C$ is the champion. In this case, by the end of the competition, teams $A$ and $B$ each lose 9 matches, while team $C$ loses at most 8 matches.

We refer to a match between one player from team $A$ and one player from team $B$ as an $AB$ match, and a match between a player from team $A$ or $B$ and a player from team $C$, where team $C$ loses, as a $C$ match. According to the competition rules, except for the first $AB$ match, the match preceding any other $AB$ match must be a $C$ match. Since there are at most 8 $C$ matches, there can be at most 9 $AB$ matches, meaning that $A$ loses to $B$ and $B$ loses to $A$ at most 9 times. Since teams $A$ and $B$ together lose 18 matches, team $C$ must win at least 9 matches.

If the first 17 matches are all won by $A_1$, then all 9 players from team $B$ and the first 8 players from team $C$ all lose. Starting from the 18th match, $C_9$ wins against all 9 players from team $A$, making team $C$ the champion with a total of 9 wins.
In summary, the champion team must win at least 9 matches.
(2) Similarly, we only need to consider the scenario where team $C$ is the champion. Since teams $A$ and $B$ together lose 18 matches, 11 of these losses are to team $C$, so there are 7 $AB$ matches. Therefore, there must be at least 6 $C$ matches, meaning team $C$ loses at least 6 matches. The competition must last at least 24 matches.

If the first 13 matches are all won by $A_1$, then $B_1, B_2, \cdots, B_7$ and $C_1, C_2, \cdots, C_6$ all lose. Starting from the 14th match, where $A_1$ competes against $C_7$, $C_7$ wins against all 9 players from team $A$ and $B_8, B_9$, totaling 11 players, and the competition ends. It is easy to see that a total of 24 matches are played, and team $C$ wins 11 matches and becomes the champion.
In summary, when the champion team wins 11 matches, the competition must last at least 24 matches.