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.

Professor Smith is D, and is a knave.

From their first statements, either A, B or E must be a knight.

IF A = KNIGHT
E = KNAVE
E lied in 1st statement, so told truth in 2nd, so
B = KNIGHT
But B calls A a knave in his second statement.

IF E = KNIGHT
B = KNIGHT
A = KNAVE
A lied in 1st statement, so told truth in 2nd, so
E = KNAVE
But E is already a knight

THEREFORE
B = KNIGHT
A = KNAVE
A lied in 1st statement, so told truth in 2nd, so
E = KNAVE
A lied in 3rd statement, so D's 1st statement is actually true, so
D = KNAVE
therefore C is the only one left, and must be a liar
C = LIAR
A told truth in 4th statement, so
D = PROFESSOR SMITH

Posted by Amber on 2005-07-18 02:15:44