## 74.

"Based on the following facts, what conclusions would you draw?" Inspector Craig asked Sergeant MacPherson:

1) If A is guilty and B is not guilty, then C is guilty.
2) C never acts alone.
3) A never goes on a job with C.
4) No one other than A, B, and C is involved in the crime, and at least one of the three is guilty.

The sergeant scratched his head and said:

- I'm afraid I can't draw much from these facts, sir. Can you, based on them, prove who among the three suspects is guilty and who is not?
- I can't, - admitted Craig, - but there is enough material to bring an irrefutable charge against one of them.

Whose guilt is beyond doubt?
74. The guilt of V is beyond any doubt. This can be proven by any of the following arguments.

Argument one. Suppose V is not guilty. Then if A were guilty, C would also be guilty by statement (1). This would mean that contrary to statement (3), A committed the crime with C. Therefore, A must be not guilty. But then, contrary to statement (2), C is the only one guilty. Hence, V is guilty.

Argument two. It leads more directly to the answer to the problem.

a) Suppose A is guilty. Then by statement (3), V and C cannot both be not guilty, so A must have an accomplice. Since C, by statement (3), could not have been an accomplice of A, it must be V. Therefore, if A is guilty, V is also guilty.

b) Suppose C is guilty. Then by statement (2), he must have an accomplice, who, by statement (3), could not be A. Therefore, it must be V.

c) If neither A nor C is guilty, then V is undoubtedly guilty!