You meet six men on a road side. The problem is that your wallet is mysteriously missing and you can't figure out if these men are truth tellers or not. So you ask a few questions and here are their answers:
Allan: "Fred stole it. Fred also hears quite well."
Barry: "Calvin is a liar. I did not steal it and I know Allan did not steal it."
Calvin: "Allan and Dwayne are both knights. Eddy stole it."
Dwayne: "Allan is a liar. I did not steal it."
Eddy: "Only 4 of us are knights. I did not steal it. I know Calvin did not steal it."
Fred: "I am deaf but read lips. Barry did not steal it."
Who stole the wallet?
P.S. You are sure that all of the men either lie or tell the truth. No one does both.
(In reply to
solution (assuming...) by Charlie)
I get the same result. Here's my reasoning:
Assume F stole it. This implies that A is a knight. If A is a knight, D is a liar. If D is a liar, then he stole it, which contradicts the assumption.
This means F didn't steal it. This implies that A is a liar. If A is a liar, then C is a liar and D is a knight. If C is a liar, then B is a knight.
There are two possibilities at this point for E. Assume E is a liar. If he is, then he stole it. Unfortunately, this contradicts the notion that C is a liar.
Now assume E is a knight. Then F must be the fourth knight. We now have the only consistent arrangement of knights and liars. To recap:
A - liar
B - knight
C - liar
D - knight
E - knight
F - knight
Now, let's figure out who the thief is:
B's statement eliminates A. F's statement eliminates B. E's statement eliminates C. D's statement eliminates D.
E's statement eliminates E. A's statement (a lie) eliminates F. This eliminates all possibilities for the thief.
re: solution (assuming...)
