81. The Trial That Followed

- I want to tell you about a trial I myself did not attend. Barmaglot told me about it.

According to Barmaglot, there were three defendants. Each of them accused one of the other two, but Barmaglot did not tell me who accused whom. However, he informed me that the first defendant was telling the truth.

- What about the second defendant? Alice asked.
- Barmaglot did not tell me whether the second defendant was telling the truth or lying.
- And the third? - Alice asked.
- Barmaglot told me either that the third defendant was lying or that he was telling the truth, but, unfortunately, I don't remember exactly what Barmaglot said. I only remember that after he told me what he told me, I was able to determine which of the three defendants was guilty, but, unfortunately, I forgot who it was.

Who of the three defendants is guilty?

![](https://cdn.mathpix.com/cropped/2024_05_21_5afa4e43618f5800e92dg-109.jpg?height=976&width=1076&top_left_y=1531&top_left_x=524)
81. The trial, following the next. Since $A$ spoke the truth and accused either $B$ or $C$, then either $B$ or $C$ is guilty, and $A$ is innocent.

The White Knight told the White King that $C$ either lied or told the truth. If the White King had been told that $C$ lied, then the White King could not determine which of the three defendants was guilty, as either $C$ could be guilty and falsely accusing $A$ (or $B$), or $B$ could be guilty and $C$ could falsely accuse $A$. Thus, if it is known that $C$ lied, there is no way to determine who is guilty: $\boldsymbol{B}$ or $C$. On the other hand, if it is known that $C$ told the truth, then he could not have accused $A$ (since $A$ is innocent). Therefore, $C$ accused $B$, and since $C$ told the truth, $B$ must be guilty. Thus, the Bandersnatch must have told the White Knight that $C$ told the truth. Then the White Knight could determine that the guilty one must be $B$.