A class basketball match was held in the eighth grade of a school. Each class has a match with other classes. The winner of each game gets 2 points, and the loser gets 1 point. If it's a draw. Two classes each get 1. Today, four students made statistics respectively, and the total scores were 53, 54, 56 and 58. After verification, one student's statistics are correct. Do you know how many classes there are in Grade Eight? There are n classes in the eighth grade.

Then the total number of n classes is * * * than (n squared -n)/2 games.

The winner of each game gets 2 points, and the loser gets 1 point. If it's a draw. Each class scored 1 point.

The winning game is always divided into 3, and the drawing game is always divided into 2.

Let the winning game be A, the drawing game be B, and the total score is S.

Then 3a+2b=s

And a+b=(n squared -n)/2.

Substitute in the box where n -n-(s-a)=0.

N and a are positive integers, and n ≥ a.

Therefore, s-a must be split into the form of m×(m- 1), where m is a positive integer.

Replace verification with 53, 54, 56 and 58 respectively.

When s=53, the minimum value of a is 1 1, which does not conform to n ≥ a.

When s=54, the minimum value of a is 12, which does not conform to n ≥ a.

When s=56, a is at least 0 and n=8.

When s=58, a is at least 2 and n=8.

You can know that there are 8 classes in Grade 8.

If all eight classes are tied, the total score is 56, and if there are two wins, the total score is 58.

I think there is something wrong with the topic. The winner of each game gets 2 points, and the loser gets 0 points.

Then 2a+2b=s

N-n-s-= the square of 0

S must be divisible into m×(m- 1), and m is a positive integer.

Solving n=8, only the total score of 56 points is correct.