Problem 3. At a tennis tournament, 5 tennis players participated. Each player played one game with each of the other players.

a) How many games were played in total at the tournament?

b) How many games did each of the players play?
Solution. Let's denote the players with the letters $A, B, C, D$ and $E$. Player $A$ played 4 games with the other four players: $B, C, D$ and $E$. Player $B$ played 4 games with players $A$ (this game has already been counted), $C, D$ and $E$. Player $C$ played four games with players $A, B$ (these games have already been counted), $D$ and $E$. Player $D$ played four games with players $A, B, C$ (these games have already been counted) and $E$. Player $E$ played four games (all of which have already been counted).

a) At the tournament, $4+3+2+1=10$ games were played.

b) Each player played 4 games.