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?
Killer: D
Accomplice: B
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There are only 12 scenarios (4 killer possibilites x 3 accomplice possibilities), and we can quickly build the table...
We can also easily go through each statement column (A, B, C, & D) and label the truth value of each statement for each scenario. (I think I got 'em all correct.)
statement
Killer Accomplice A B C D
A B T T T T
A C T T T T
A D T T T F
B A T T T T
B C F T T T
B D T F F F
C A T T T T
C B F T T T
C D T T T F
D A T T T F
D B T F T F
D C T T T F
Since the only one with two False statements (let alone two false statements that correspond to the guilty parties), is:
D is the killer and B is the accomplice.
full solution
