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Professor Smith (Posted on 2005-07-13) Difficulty: 2 of 5
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.

See The Solution Submitted by Dustin    
Rating: 3.3750 (8 votes)

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Solution Solution and spoiler | Comment 1 of 16

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 2005-07-13 06:14:01
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