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Amery, Brant, and Fredo are liars, while Cuthbert, Derek, and Everard are knights.
Number the six statements 1-6 and nickname the men A-F. Start by assuming E is a liar. Then statements 2 and 3 are false, making B and C liars. If D is a knight, statement 4 is true, making A a liar and statement 1 false. Since C is a liar, F must be a knight, making statement 6 true, making A a knight, which contradicts an earlier assumption. Therefore D is not a knight. If D is a liar, statement 4 is false, and since B is a liar, A must be a knight, so statement 1 is true, making F a liar, so statement 6 is false, and since A is a knight, D must be a knight, which contradicts the original assumption. Since D can be neither a liar nor a knight when starting from the assumption that E is a liar, this assumption must be wrong. Therefore E is a knight and statement 5 is true, so C and D are also knights. From statement 4, A and B are both liars, so from statement 2, F must be a liar. In summary: the liars are Amery, Brant, and Fredo, and the knights are Cuthbert, Derek, and Everard. |
