Professor Smith has been studying the knights, knaves, and liars in their villages, and is currently living among them. You and your guide (who is a knight) approach a fork in the road and see five people standing in a line facing you. Your guide tells you there is one person he knows to be a knight, one person he knows to be a liar, one person he knows to be a knave, one he doesn't know at all, and Professor Smith. They said:
A: I am a knight.
B: I am a knight.
C: I am a knave.
D: I am a knave.
E: I am a knight.
A: E is a knave.
B: A is a knave.
C: D is a liar.
D: C is a knave.
E: B is a knight.
A: D's first statement is a lie.
B: C's first statement is a lie.
C: A's second statement is a lie.
D: B's third statement is true.
E: C's second statement is true.
A: D is Professor Smith.
B: C is not Professor Smith.
C: I am Professor Smith.
D: A is Professor Smith.
E: I am not Professor Smith.
Which one is Professor Smith? Remember: Knights always tell the truth. Liars always lie. Knaves alternate between truths and lies. Professor Smith is one of these three types, but you don't know which.
A Knave
B Knight
C Liar
D Knave  Professor Smith
E Knave
Notation A1 is A's first comment. B2 is B's second comment.
If D1 is true then D is a knave and D2 is false by alternating trues and false. If D1 is false then D is a liar and D2 is also false. Thus D2 is a lie.
Since D2 is a lie C1 is a lie and C is a liar.
Since C is a liar, from C2, D is not a liar and must be a knave.
Since C is a liar, from C3, A2 is the truth and E is a knave.
With E being a knave, E1 is a lie and thus E2 is the truth making B a knight.
Since B is a knight, from B2, A is a knave.
With A being a knave, and A1 being false, A2 and A4 must be true, and D is Professor Smith.

Posted by Leming
on 20050713 06:14:01 