1. In a chess tournament, 10 players participated. Each player played one game with each of the other players.

a) How many games did each individual player play?

b) How many games of chess were played in total at the tournament?

Explain your answers.
First method:

Let's mark the players with numbers from 1 to 10. List the possibilities for one of the players (since the choice of player does not affect the result), for example, for player number 1:

1 and 2, 1 and 3, 1 and 4, 1 and 5, 1 and 6, 1 and 7, 1 and 8, 1 and 9, 1 and 10.

$1 \text{POINT}$

Since it doesn't matter which player we observed, we conclude that each player will play 9 matches.

$1 \text{POINT}$

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