Each of the suspects made a statement, but only one of the statements was true.
Dick said, "I didn't do it."
Jack said, "Dick is lying."
Sally said, "Jack is lying."
Jimmy said, "Jack did it."
Who committed the crime?
You have one of two ways to approach this problem.
One way is to assume that one of the statements is true and that the others are false, and see what you can conclude from that. For example, suppose that Dick's statement is true. Then, Jack's is false, but Sally's is true, which contradicts the information that only one statement is true. So some other statement must be the true one, and Dick's is false. So, Dick committed the crime!
Another way to attack the problem is to assume that
one of the suspects committed the crime and determine
which statements are true and false. Suppose Dick was
the criminal. Then Dick was lying. So his statement
was false, Jack's was true, Sally's was false, and
Jimmy's was false. Since there are three false
statements and one true, this fits and Dick was the
criminal! (Of course, you should check the other
possibilities in case there were two criminals!)
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