The cookie thief and the single liar

Question

One cookie is missing from the jar. Exactly one of four children took it, and exactly one of their statements below is a lie (the other three are true).

Ana: "Ben took the cookie."
Ben: "Cy took the cookie."
Cy: "Ben is lying."
Dee: "I did not take the cookie."

Who took the cookie?

Accepted Answer

Notice that Ben and Cy directly contradict each other. Ben says "Cy took it"; Cy says "Ben is lying." If Ben is telling the truth, then Cy's accusation that Ben is lying is false. If Ben is lying, then Cy's statement is true. Either way, exactly one of Ben and Cy is the liar, the two of them can never both be truthful or both be lying. Since the puzzle allows only one lie in total, and that lie is already used up by the Ben/Cy pair, Ana and Dee must both be telling the truth. Ana is truthful, and Ana says "Ben took the cookie." So the thief is Ben. Check for consistency: - Ben took it, so Ben…

The cookie thief and the single liar

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