76. The Case of the Four.

This time, four suspects in a robbery were called for interrogation: A, B, C, and D. Indisputable evidence has proven that at least one of them is guilty and that no one other than A, B, C, and D was involved in the robbery. Additionally, the following facts were established:

1) A is undoubtedly not guilty.
2) If B is guilty, then he had exactly one accomplice.
3) If C is guilty, then he had exactly two accomplices.

Inspector Craig was particularly interested in determining whether D was guilty or not, as D was a dangerous criminal. Fortunately, the facts provided above are sufficient to determine the guilt or innocence of suspect D.

So, is D guilty or not?

## B. COULD YOU HELP?

Inspector Craig is often seen in the courtroom, where he follows all the twists and turns of the trial with unwavering attention. Craig is not only interested in the cases in which he has been involved in the investigation. Listening to any case serves as a kind of logical exercise for him: after hearing the arguments of both sides, the inspector strives to establish the truth through logical reasoning. Here are a few curious cases he has witnessed in the courtroom.
76. If B is guilty, then by statement (2) exactly two defendants are involved in the crime. If C is guilty, then by statement (3) three defendants are involved in the crime. Since neither can be true, at least one of B and C is not guilty. Defendant A is also not guilty, so there cannot be more than two guilty individuals. Therefore, C did not have exactly two accomplices, and by statement (3) defendant C must be not guilty. If B is guilty, then he had exactly one accomplice. It must be D (since A and B are both not guilty). If B is not guilty, then A, B, and C are not guilty. Then D must be guilty. Thus, regardless of whether B is guilty or not, defendant $\mathrm{D}$ must be guilty. Therefore, D is guilty.