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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. | Comment 5 of 16 |

A = Knave lie first

B = Knight

C = Lian

D = Knave (The Professor) truth first

E = Knave lie first

From the first comment you know that C and D CANT be knights... So you assume that A is a knight. first...

If E is a knave then his first statement is false and his pattern goes L/T/L/T ( just like A if we assumed that A was a knave)... then you go on... If D's first statement was  lie then D must be a Liar or knave because he couldnt be a knight. and then A truthfully says that D is Prof. Smith.. ( the problem only asks for that much so you technically could stop there....)

So if you assume that E is telling the truth on the second statement then B must be the knight (keep that in mind).  E's third statement must be a lie in sayin that C's statement is true. and E's fourth statement must be the truth... (still works)

So far A is a knight  D is a liar or knave and E is knave and D is the (prof.)So if D is a liar then C MUST also be a liar because C cant be a knight and cant be a knave if D is lying (statement 2) Also if D is a liar then B cant be a knight. but D being the Prof. still holds true...

Next C as a def Liar.  First statement is a lie. The second statement means that D is a Definite Knave because C is a def Liar.  A second statement has to be true as well and C cant be the prof.  Now because A's third statement A MUST be a knave in the same pattern as E (L/T/L/T)

Now we have  A def knave (L/T/L/T) , B unknown , C as a def. Liar, D as a def. knave (T/L/T/L), and E as a def. Knave like A

If D is a def. Knave then his pattern must be T/L/T/L opposite of E.  D's second statement corresponds to that.  The third says that B third statement is true... meaning that B can only be a Knight or a T/L/T/L knave. and D's fourth statement is a lie

Since we know that there was at lease ONE, the ONLY KNIGHT is B... Since you know that A is a knave and his pattern is l/t/l/t then his last statement about D being the professor has to be true..



  Posted by Brandon on 2005-07-13 22:50:47
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