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Murder by Logic (Posted on 2004-03-05) Difficulty: 3 of 5
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?

  Submitted by Federico Kereki    
Rating: 3.7692 (13 votes)
Solution: (Hide)
D's declaration is worthless: were he innocent or guilty he could have said so.

Suppose C was guilty: as he would lie, then B should be the killer, but D would have to be involved too, making three guilty parties; it follows that C was innocent.

Suppose B was innocent: A could be innocent or guilty. If A was innocent, then C would have to be guilty, but we showed C was innocent, so A couldn't be innocent. If A was guilty, since he lied, B and C must have been guilty -- and that's contradictory. As A cannot be either guilty or innocent, B cannot be innocent; he is guilty.

Since B is guilty, A must be innocent, and C must be too (which we had already proved).

We have now that B and D are guilty, but if B was the killer, then D would be innocent (as C said) so B must have been the accomplice, and D the killer.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2008-05-15 06:17:09
answerK Sengupta2007-11-10 04:44:12
re: Help me out...Penny2004-06-25 16:05:08
re: another solution I think...Tristan2004-06-24 18:20:27
another solution I think...mic2004-06-24 17:41:06
Help me out...Jeremy Trenary2004-05-28 19:44:56
alternate solutionDaymiris Gell2004-05-17 20:30:14
Think there's something wrong..paul priest2004-05-07 09:32:59
SolutionSolution!Galendir2004-03-21 16:23:57
re(3): full solutionMatthew Pianalto2004-03-10 03:49:37
re(2): full solutionSilverKnight2004-03-10 03:15:52
re: full solutionMatthew Pianalto2004-03-09 21:18:16
re(2): solutionPenny2004-03-09 16:39:43
Some Thoughtsre: solutione.g.2004-03-09 14:48:09
Solutionsolutionpaul2004-03-08 21:32:45
the answer?Sunwoo Lee2004-03-08 20:28:45
SolutionSolutione.g.2004-03-08 14:00:00
Yes it does, DebPenny2004-03-08 06:00:16
Does solution have to be more detailed then this?Deb2004-03-07 19:47:19
re: if d is not the killer...Sam2004-03-06 13:27:11
if d is not the killer...Chandrakant2004-03-06 11:00:17
SolutionSolutionPenny2004-03-05 16:05:02
Solutionfull solutionSilverKnight2004-03-05 15:17:48
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