perplexus.info :: Logic : Murder by Logic

Murder by Logic (Posted on 2004-03-05)

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
Puzzle Solution	K Sengupta	2008-05-15 06:17:09
answer	K Sengupta	2007-11-10 04:44:12
re: Help me out...	Penny	2004-06-25 16:05:08
re: another solution I think...	Tristan	2004-06-24 18:20:27
another solution I think...	mic	2004-06-24 17:41:06
Help me out...	Jeremy Trenary	2004-05-28 19:44:56
alternate solution	Daymiris Gell	2004-05-17 20:30:14
Think there's something wrong..	paul priest	2004-05-07 09:32:59
Solution!	Galendir	2004-03-21 16:23:57
re(3): full solution	Matthew Pianalto	2004-03-10 03:49:37
re(2): full solution	SilverKnight	2004-03-10 03:15:52
re: full solution	Matthew Pianalto	2004-03-09 21:18:16
re(2): solution	Penny	2004-03-09 16:39:43
re: solution	e.g.	2004-03-09 14:48:09
solution	paul	2004-03-08 21:32:45
the answer?	Sunwoo Lee	2004-03-08 20:28:45
Solution	e.g.	2004-03-08 14:00:00
Yes it does, Deb	Penny	2004-03-08 06:00:16
Does solution have to be more detailed then this?	Deb	2004-03-07 19:47:19
re: if d is not the killer...	Sam	2004-03-06 13:27:11
if d is not the killer...	Chandrakant	2004-03-06 11:00:17
Solution	Penny	2004-03-05 16:05:02
full solution	SilverKnight	2004-03-05 15:17:48

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (22)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info