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.

We know that there is a least one knight, one knave and one liar. Knights are easiest to determine so we'll start there.

From first statements only A, B and E can be knights.

If A was a knight:
E is a knave (2A)
B is a liar (2B & 1B)
But E 1st and 2nd statments are both lies therefore E can not be a knave which is a contradiction therefore A is not a knight.

If E was a knight:
B is a knight (2E)
D is a liar (3E & 2C)
C is a liar (3B & 1C)
But C 2nd statement says D is a liar which means D is not a liar which is a contradiction therefore E is not a knight.

B must therefore be a knight and you can work out everyone else from this:
A is a knave (2B)
C is a liar (3B & 1C)
E is a knave (1A & 2A)
D is a knave (3A & 1D

Looking A's 4th statement which is true D is Professor Smith who is a knave.

Summary:
A - knave (lie-truth-lie-truth)
B - knight
C - liar
D - knave (truth-lie-truth-lie) - Professor Smith
E - knave (lie-truth-lie-truth)

Posted by Lisa on 2005-07-13 12:21:51