## 84. And One More Case

- I remember another trial I attended as if it were today, - began the White Knight. - There were three defendants, and only one of them was guilty. I remember that the first defendant accused the second, but I completely forgot what the second and third defendants said. I also remember that last week the Black Queen asked me to tell her about the trial, and I told her one more fact that I can't recall now. Either I told the Black Queen that the guilty one was the only defendant who lied, or I told her that the guilty one was the only defendant who told the truth. But I distinctly remember that the Black Queen was able to determine who was guilty through logical reasoning.

Who is guilty?
84. And one more case. We know that $A$ accused $B$, but we do not know what $B$ or $C$ said. Suppose we had additional information that the guilty one is the only one of the three defendants who gave false testimony. Then the guilty one could be any of the three defendants. It would be impossible to determine exactly which one of the three is guilty. On the other hand, if we knew that the guilty one is the only one of the defendants who told the truth, then we could conclude that $A$ cannot be guilty (since if $A$ were guilty, then by accusing $B$, he would have told the truth, which in turn would mean that $B$ is guilty) and $B$ cannot be guilty (since if $B$ were guilty, then $A$ would be innocent and, therefore, would have told the truth about $B$). Therefore, the guilty one must be $C$.

Thus, the Black Queen could have learned from her conversation with the White Knight only that the guilty one is the only one of the defendants who gave truthful testimony (otherwise, the Black Queen could not have determined who is guilty).

Therefore, $C$ is guilty.