The Question
A football tournament involves 6 teams and each team plays all the other teams once. If a team wins a match it gets 3 points, with the loser getting 0; if a match is drawn then both teams get 1 point. In this particular tournament, it was noticed that every drawn game was between teams with a different number of points on the board at the time of play.
What is the maximum possible number of drawn games?
This is at the level of a secondary national mathematics competition.
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