, 2015

Combinatorics Difficulty 2.4 Junior Find the answer Slovenia

In a football tournament participated $n$ teams. Each team played exactly one match with each other team. There was a total of $2015n$ matches played in the tournament. How many teams participated in the tournament?

Pick one

Solution

There was a total of $\binom{n}{2}$ matches played in the tournament, thus $\binom{n}{2} = \frac{n(n-1)}{2} = 2015n$ . From this we deduce $n = 4031$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.