3. Once, a detective had to interrogate three witnesses of a robbery: John White, Sam Gray, and Bob Black. John insisted that all of Sam's statements were lies, while Sam kept repeating that Bob was lying. Bob, for his part, tried to convince the detective not to believe either White or, especially, Gray. The detective, being a clever and intelligent person, asked all three to be silent and, without asking any more questions, quickly determined who to trust and who not to. Who among the witnesses was not lying?
Answer: Sam Gray.

Solution. From the condition of the problem, it is clear that the statements of each of the witnesses were made regarding the statements of the other two witnesses. Let's consider the statement of Bob Black. If what he says is true, then Sam Gray and John White are lying. But from the fact that John White is lying, it follows that not all of Sam Gray's statements are a complete lie. And this contradicts the words of Bob Black, whom we decided to believe and who claims that Sam Gray is lying. Thus, Bob Black's words cannot be true. Therefore, he lied, and we must recognize Sam Gray's words as true, and, consequently, John White's statements as false. Answer: Sam Gray did not lie.

Evaluation criteria.

- A complete and correct analysis of the situation in the problem and a correct answer given - 7 points.
- A complete and correct analysis of the situation, but for some reason an incorrect answer is given (for example, instead of who did NOT lie, the answer indicates those who lied) - 6 points.
- A correct analysis of the situation, but for some reason a correct answer is not given (for example, it is proven that Bob Black lied, but no further conclusions are made) - 4 points.
- A correct answer is given and it is shown that it satisfies the condition of the problem (a check is performed), but it is not proven that the answer is unique - 3 points.
- Only a correct answer is given - 1 point.
- A correct answer is given with incorrect reasoning - 0 points.