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Who Was the Thief?

A did it. Since only one of the four told the truth, B and D, who contradicted each other, couldn't be right or wrong at the same time. In other words, one of them must be telling the truth. And, if the truth-tell was either B or D, then A and C both lied. C lied when he said "B did it," and A lied when he said "I didn't do it." So A was the culprit.
 

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