Step-by-step explanation:
6 players.
every player plays 2 games against every other player.
so, for each player there are 5 "other players" and everybody plays therefore 10 games.
the maximum number of points to get is 10×2 = 20 points.
the question is now not what is the minimum number of points a champion can have.
the question is rather what is the minimum number of points to guarantee the win of the championship no matter how the others played.
so, the study case scenario for the winner is to have only one real competitor for the title.
both players win every game against the other 4 players.
that is already 2×4×2 = 16 points.
and now it all depends on the 2 games against each other. to be sure, the winner needs at least 1 win and 1 tie in these 2 games. that are 3 more points.
so, to be absolutely sure, the champion needs to have at least 16+3 = 19 points.
