Professor Z was killed by one of his four students, who was helped by another of the four. His students declared:
A: If B is guilty of something, then C must be innocent.
B: If A is innocent, then C must be guilty.
C: If B was the killer, then D must have had nothing to do with the crime.
D: I am innocent.
As everybody should know, guilty parties always lie, and innocent people always tell the truth. Who killed the professor, and who was his accomplice?
D was the killer, B the accomplice, and A and C are innocent.
(I did NOT read SilverKnight's solution before I arrived at this.)
Explanation: Three of the statements are conditional statements, and a conditional statement "If X, then Y" is always true except in the case where X (the antecedent) is true and Y (the consequent) is false.
If A is guilty, then A's conditional statement "If B is guilty of something, then C must be innocent" is false; hence the antecedent must be true and the consequent false. Therefore B is either the killer or the accomplice, and C is either the killer or the accomplice. Then there are three guilty people: A,B and C. This violates the puzzle conditions.
If C is guilty, then C's conditional statement "If B was the killer, then D must have had nothing to do with the crime" is false. Then B was the killer (true antecedent) and D helped him (false consequent). Then there are three guilty parties: B,C and D. This violates the puzzle rules.
So A and C are innocent, and then B and D are guilty.
B's statement is false. Therefore A is innocent (true antecedent) and C is innocent (false consequent).
D's statement is false: D is guilty.
A's conditional statement "If B is guilty of something, then C must be innocent" is true.
C's conditional statement "If B was the killer, then D must have had nothing to do with the crime" is true. Either both antecedent and consequent are true, or both are false, or the antecedent is false and the consequent is true. Therefore (1) B was the killer and D was innocent; or (2) B was not the killer and D was involved in the murder; or (3) B was not the killer and D had nothing to do with it. Only (2) hasn't been eliminated so far.
Therefore D was the killer, B the accomplice, and A and C are innocent.
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Posted by Penny
on 2004-03-05 16:05:02 |
Solution
