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.
1) Assume that Allan is a knight, then Fred hears well and stole the wallet. Since Fred claims to be deaf then he is a liar - but he claims that Barry didn't steal the wallet, which means he did. The contradictions shows us that Allan is a liar, Fred is a knight, and Fred and Barry are innocent.
2) Dwayne remarks that Allan is a liar (which is true, so his second statement proves his innocence.
3) Calvins statement that BOTH Allan and Dwayne are knihts is a lie, proving that Eddy is innocent.
4) With two confirmed liars, there can be at most 4 knights, so the only/exactly controversy in Eddys comment is moot.
5) We previously know that Eddy is innocent (as Calvin is a liar), so his comment to that effect proves him to be a knight. This leads to the conclusion that Calvin in innocent, and to complete the group with 4 knights Barry must also be a knight. This eliminates our final suspect Allan.
In summary, using each characters first initial, and k=knight l=liar, we have the following;
A,l proves F innocent
B,k proves B and A innocent
C,l proves E innocent
D,k proves D innocent
E,k proves C innocent
F,k confirms B innocent
What does this mean? Well there is no one person responsible among them for the theft. Could be you've lost it or left it at home, could be someone else, or maybe there is a possible solution where the members have cooperatively stolen your wallet. Haven't checked this out yet, but to explain my thinking...
re-assuming that Fred is a knight, his second comment could be construed as true if Barry AND Mr. X. stole the wallet.
I'm not sure this will produce a solution either, but if this isn't the idea, I've nothing else to go on.
hmm.
