2. $A, B, C, D, E$ five chess players are competing together. So far, $A$ has played four games, $B$ has played three games, $C$ has played two games, $D$ has played one game. How many games has $E$ played?
2. Represent five chess players with five vertices. If two players have played against each other, draw a line between them, resulting in the graph below. Since $A$ has played four games, it is connected to $B$, $C$, $D$, and $E$; since $D$ has only played one game, it is only connected to $A$; since $B$ has played three games but not with $D$, $B$ is connected to $A$, $C$, and $E$ but not to $D$; $C$ has played two games, which can only be with $A$ and $B$; so $E$ has not played with $C$ or $D$, but has played one game each with $A$ and $B$, hence $E$ has played two games.