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.

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