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

The best solution was submitted by 구재현 (전산학부 2017학번, +4). Congratulations!

Here is the best solution of problem 2021-24.

Other solutions were submitted by 이도현 (수리과학과 2018학번, +3), 이재욱 (전기및전자공학부 2018학번, +3), 이충명 (기계공학과 대학원생, +3), 이호빈 (수리과학과 대학원생, +3), 전해구 (기계공학과 졸업생, +3). Late solutions were not graded.