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Mathematics of criminal speculation
The answers of the four people are as follows

A: No.

: d yes

C: Yes.

D is not.

Because B and D contradict each other, one of them must be false. The other one is true.

If B is true, that is, D is a criminal, then A is also true. What two people say is true, so if B is true, it is wrong.

Then d is the truth, and A\B\C is a lie. Because A says A is true, A is a criminal.