In a remote island there are only two types of people that live on it, Knights and Liars. Knights always tell the truth. Liars always speak falsely.
Five suspects are interrogated in connection with a murder. Their statements are as follows:
Al: "Cal and Dan are lying."
Ben: "Al and Elmer are lying."
Cal: "Ben and Dan are lying."
Dan: "Cal and Elmer are lying."
Elmer: "Al and Ben are lying."
Which suspect do you know for certain to be a liar?
Consider the statement: "F and G are lying". This is a lie if EITHER F or G (not necessarily both) is telling the truth.
Assume that A is telling the truth.
Then C and D are both lying (based on A's statement).
But D agrees that C is lying, so D's statement being false implies that E is telling the truth.
But E says that A is lying, which is a contradiction
Our initial assumption is wrong. We know that A is lying.
We could stop here,but I will rule out other possibilities in a later post.
Edited on February 26, 2013, 1:30 pm