MHB Who Solved the Crime in the Latest Problem of the Week?

[Ackbach]

Here is this week's University POTW.

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Four suspects of a crime made the following statements to the police:

Andy: Carl did it.
Bob: I did not do it.
Carl: Dave did it.
Dave: Carl lied when he said I did it.

Given that one of them "did it" and that exactly one of them told the truth, who did it?

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[Ackbach]

Fallen Angel and Kiwi both submitted correct solutions to this week's University Problem of the Week. I include Kiwi's solution:

Spoiler

Numbering the statements:

I Andy: Carl did it.
II. Bob: I did not do it.
III. Carl: Dave did it.
IV. Dave: Carl lied when he said I did it.

If Dave did it then statements II and III would both be correct so Dave did not do it.
If Carl did it then statement s I and II are true so Carl is innocent.
If Andy did it then statements II and IV are both correct so Andy is also innocent.
Bob did it and the only correct statement is IV.