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.
If the statement "only 4 of us are knights" means that exactly 4 are knights then the following logic applies:
C and D cannot both be knights as A can be only a knight or a liarnot both.
But if E stole it, they'd both be knights, so
E did not steal it.
E is a knight since he truthfully says he did not steal it.
So
C did not steal it based on Eddy's word. I also take it that "only 4 of us are knights" means that exactly 4 are knights, so exactly 2 are liars.
If D were a liar and actually took it, then so would A and C be liars as they name someone else, and that's too many liars. So
D is a knight and
D did not steal it.
C is in fact a liar as he claims E stole it. So A and D are not both knights, though D is one, so
A is a liar, not a knight. So
F did not steal it.
Since only A and C are liars,
B and F are also knights, so
B did not steal it and
A did not steal it.
This rules out all the witnesses as being the thief, none of A through F stole the wallet.

Posted by Charlie
on 20030610 09:52:36 