Question 153
Before 1995, in Football Championship of Ukraine in all leagues the team received 2 points for winning, 1 point for a draw and 0 points for a defeat. Since 1995, winning would give 3 points to the team, 1 point for a draw and 0 for a defeat. Football Federation has decided to transpose all the championships that were held in all leagues during all years to the new grading system, believing that the distribution of places will not change drastically. However, it turned out that in the championship in 1927 in one of the regional leagues $n$ teams held the championship in one round, i.e. each team played with each another once. There team "A" gained the largest amount of points, and the team "B" gained the least number of points. But after the points calculation according to the new rules team "B" gained the most points, and team "A" gained the least amount of points. For which the least $n$ this could happen?
Here the fact that the team has the lowest or the highest score, means that no other team gained this number of points.
Here the fact that the team has the lowest or the highest score, means that no other team gained this number of points.