## Task 4 - 140514

Some students from a 5th grade class held a chess tournament. Each participant played exactly 2 games against every other participant. In total, 3 games were played each day for 24 days.

Determine the number of participants in this tournament!
There were a total of $24 \cdot 3=72$ games.

If everyone plays 2 games against everyone else, there are $n \cdot(n-1)$ games with $n$ participants. This leads to the equation $n \cdot(n-1)=72$, which is only satisfied by $n=9$ in the domain of natural numbers (since there can only be a natural number of participants). This solution is found through systematic trial and error.

To do this, one checks the products $n(n-1)$, i.e., $2 \cdot 1, 3 \cdot 2, \ldots$ until reaching $9 \cdot 8=72$.

A solution using the quadratic formula for $n^{2}-n-72=0$ with $n_{1}=9, n_{2}=-8$ is generally not possible for 5th-grade students.