2. On an island, there live knights and scoundrels. Knights always tell the truth, and scoundrels always lie. You encounter five people on the island, and you know that four of them are knights and one is a scoundrel, but you don't know who. They make the following statements about the islanders:

- A: "All scoundrels wear shoe size 40."
- B: "All people who wear shoe size 40 have a goldfish."
- C: "All people with a goldfish are scoundrels."
- D: "I wear shoe size 40."
- E: "I have a goldfish."

Who among them is the scoundrel?
A) A
B) B
C) $\mathrm{C}$
D) D
E) E
A2. C) C The statements of $\mathrm{C}$ and $\mathrm{E}$ cannot both be true, because then E would be a villain, which contradicts the fact that he was telling the truth. Similarly, the statements of $B, C$ and $D$ cannot all be true at the same time, because then $D$ would be a villain while he was actually telling the truth. The villain must therefore be $\mathrm{C}$ or $\mathrm{E}$, and at the same time B, C or $\mathrm{D}$. The only possibility is therefore that $\mathrm{C}$ is the villain.

Finally, we note that the situation where only $\mathrm{C}$ is a villain is indeed possible. If only $\mathrm{C}$ and $\mathrm{D}$ have shoe size 40, $\mathrm{C}, \mathrm{D}$ and $\mathrm{E}$ have a goldfish, and $\mathrm{C}$ is the only villain, then the statements of $\mathrm{A}, \mathrm{B}, \mathrm{D}$ and $\mathrm{E}$ are all true and the statement of $\mathrm{C}$ is false.