## Problem of the week

### 2021-24 The squares of wins and losses

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
$\sum_{i\in [n]} a_i^2 = \sum_{i\in [n]} b_i^2.$