Task 1. At a chess tournament, 12 chess players participated. Each chess player played 3 games with each other chess player. How many games were played at the tournament.
Solution. 12 chess players participated in the tournament, and if each played one game with each of the other 11 players, then since the game between $X$ and $Y$ is the same as the game between $Y$ and $X$, we conclude that in the product $12 \cdot 11=132$ each game is counted twice. Therefore, if each chess player played one game with every other player, the number of games played is equal to $\frac{12 \cdot 11}{2}=66$. However, each played 3 games with each other, so the number of games played is equal to $3 \cdot 66=198$.