6.38 25 chess players participate in a chess competition, their strengths are all different, and in each match, the stronger one wins. How many matches are needed at least to determine the two strongest players?

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[Solution] Since the 25 players have different strengths and the stronger player always wins in each match, anyone who loses a game in the process is not the strongest player. To minimize the number of matches, the tournament should be conducted in an elimination format. Thus, after 24 matches, the strongest player $A$ will be determined.
25 players participating in an elimination tournament will require a total of 5 rounds. Player $A$ can appear at most 5 times, defeating 5 players. The second strongest player must be among these 5. These 5 players will then engage in an elimination tournament to select the strongest, which will require 4 matches. Therefore, to determine the two strongest players, a minimum of 28 matches are needed.