Two thieves have being working together for years. Nobody knows their identities, but one is known to be a Liar and the other a Knave. The local sheriff gets a tip that the bandits are about to commit another crime. When the sheriff arrives at the seen of the crime, he finds three men, A, B, and C. C has been stabbed with a dagger. He cries out, “A stabbed me” before anybody can say anything else; then, he falls down dead from the stabbing.
Not sure which of the three men are the crooks, the sheriff takes the two suspects to the jail and interrogates them. He gets the following information.
A’s statements:
1. B is one of the crooks.
2. B’s second statement is true.
3. C was telling the truth.
B’s statements:
1. A killed the other guy.
2. C was killed by one of the thieves.
3. C’s next statement would have been a lie.
C’s statement:
1. A stabbed me.
The sheriff knows that the murderer is among these three people. Who should the sheriff arrest for killing C?
All three people agree on the fact that A killed C (from A3, B1, C1).
At least one of them is a Liar, which makes this statement false. We
also know that there are no knights amongst A,B and C.
A3 is false, which implies that A1 must also be false. Now we know that
A and C were the crooks. B1 was false, which implies that B3 would also
have to be a lie. This implies that C was the crook which was a Knave,
and A the Liar. This makes A2 false, which means that B is also a Liar.
C was not killed by the thieves (not by A, and not suicide), so he was
killed by B.
Solution
