3. On Misfortune Island, a table tennis tournament was held in a round-robin format (i.e., everyone played against everyone else once). After each match, both participants separately approached the Chief Referee and reported the result. Among the participants, there were only three types of people: knights, who always tell the truth, liars, who always lie, and politicians, who always say what is advantageous to them—each politician claimed after each match that they had won.

After the tournament, it turned out that the Chief Referee, incognito, had attended several matches, as a result of which he was lucky enough to not only be able to determine the results of all the matches but also to find out that there were exactly six politicians. What is the minimum number of matches he could have attended?

(There are no draws in table tennis. The Chief Referee did not know in advance which players belonged to which type, and did not receive information in any other way except as described in the condition)
Answer: 16

## Examples of answer recording:

17

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