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Problem of the week

There are \(n\) people participating to a chess tournament and every two players play one game. There are no draws. Let \(a_i\) be the number of wins of the \(i\)-th player and \(b_i\) be the number of losses of the \(i\)-th player. Prove that
\[\sum_{i\in [n]} a_i^2 = \sum_{i\in [n]} b_i^2.\]