Task B-3.8. In a basketball tournament, 8 teams participated and each played one match against each other. For a win, 2 points are awarded, and for a loss, 0 points (no match ended in a draw). The teams accumulated 14, 12, 8, 8, 6, 4, 2, 2 points respectively. How many matches did the last 4 teams lose to the first 4 teams?
## Solution.

The last four teams played $\frac{4 \cdot 3}{2}=6$ matches against each other and collected a total of 12 points (each of which belonged to one of the last 4 teams).

(3 points)

Since they collectively earned $6+4+2+2=14$ points, we conclude that the last 4 teams scored 2 points against the first 4 teams, meaning they won only one match against the first four teams.

(3 points)

The total number of matches played between the first four and the last four teams is $4 \cdot 4=16$.

Of these, they lost only one match.

(1 point)

Therefore, the solution is:

The last four teams lost 16 - $1=15$ matches to the first four teams.

## ZUPANIJSKO NATJECANJE IZ MATEMATIKE

## 4th grade - high school - B category

## March 15, 2010.

IF A STUDENT HAS A DIFFERENT APPROACH TO SOLVING THE TASK, THE COMMITTEE IS OBLIGED TO GRADE AND EVALUATE THAT APPROACH IN AN APPROPRIATE MANNER.