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Problem 308

Combinatorics Difficulty 2.4 Multiple choice National Math Olympiad – First Round · Slovenia · 2015

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

Official 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 $n = 4031$ .

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