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.
Suppose an inhabitant says, "I am a knave." Then, they are not a knight, so they are either a knave or a liar. If they are a knave, then their next statement and every other statement is false. If they are a liar, then every statement is false. C and D both claim to be knaves, so their second and fourth statements are false. Therefore, D is not a liar and C is not a knave, so D is a knave and C is a liar. Also, their fourth statements are false, so Professor Smith is neither A nor C.
Since C is a liar, C's third statement is false, so A's second statement is true and E is a knave. E's third statement is false because C always lies, so E's second statement is true and B is a knight. Since B says that A is a knave, A must really be a knave. A's first statement is false, so A's fourth statement is true. That means that D is Professor Smith.
D:knave (Professor Smith)
Edited on May 21, 2011, 11:59 am
Posted by Math Man
on 2011-05-21 11:53:41