A logical inference puzzle. One variety goes like this:
Some of the natives of a South Pacific island are pure-blooded and the rest are half-breeds, but they all look alike. The pure-blooded always tell the truth, but the half-breeds always lie. A visitor to the island, meeting three natives, asks them whether they are full-blooded or half-breeds. The first mumbles something inaudible. The second, points to the first and says, "He says that he is pure-blooded." The third, pointing to the second, says, "He lies." Knowing that only one is a half-breed, the visitor decides what each of the three are.
Here's a slightly different version of the same type of puzzle:
four men, one of whom was known to have committed a crime, made the following statements when questioned by the police:
Archie: Dave did it.
Dave: Tony did it.
Gus: I didn't do it.
Tony: Dave lied when he said I did it.
If only one of these four statements is true, who is guilty? On the other hand, if only one of these four statements is false, who is guilty?