A person was killed. There are 4 suspects.
A says C is the killer. B says C is the killer. C says that B is lying. D says that it wasn't him.
There is only one person telling the truth. Who is this person, and why?
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1$\begingroup$ Are you sure this isn't supposed to be [lateral-thinking] rather than [logical-deduction]? Because there's another solution that I think fits more under the former tag than the latter, and I suspect that's what you're going for. $\endgroup$– Deusovi ♦Oct 12, 2019 at 19:31
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1$\begingroup$ This really only asks who is speaking the truth. Didn't you also intend to ask who the killer is? Because that's also deducible, as @WhatsUp does. $\endgroup$– GloweyeOct 14, 2019 at 13:37
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$\begingroup$ Possibly related: puzzling.stackexchange.com/questions/57401/… $\endgroup$– MechMK1Oct 14, 2019 at 14:41
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$\begingroup$ What is the answer? $\endgroup$– ahmedOct 18, 2019 at 10:28
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10 Answers
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The person telling the truth is:
C
because:
A and B cannot both tell the truth, so they are both lying. B and C cannot both be lying, so C is telling the truth
and consequently, the killer is:
D, because D is lying.
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This answer's a little eccentric, but bear with me. (Warning: this answer would fit a lateral-thinking puzzle, but since it is not explicitly a non-lateral-thinking puzzle, just treat this as light-hearted entertainment.)
There is no killer.
Suppose the narrator is telling the truth that there is only one person telling the truth.
Then the narrator is the truth teller, and all the others must be liars. But since B is among the liars, C's statement is true, which contradicts the supposition (we now have 2 truth tellers: the narrator and C).
So the narrator is a liar, and the initial statement "A person was killed" is false. Since nobody was killed, there is no killer. :P
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$\begingroup$ But then you still haven't solved the puzzle of who's telling the truth. $\endgroup$ Oct 30, 2019 at 18:26
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$\begingroup$ @AdmiralJota There's an argument for C or D: no killer => B is lying and D isn't the killer. However, if the narrator is lying, the whole thing is compromised. There might not even be people called A, B, C or D. $\endgroup$– LawrenceOct 30, 2019 at 18:30
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2$\begingroup$ Tsk. You had the perfect opportunity to claim that role for yourself... $\endgroup$ Oct 30, 2019 at 18:57
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$\begingroup$ @AdmiralJota Haha! That would have been icing on the cake. Ah, well, what’s done is done. $\endgroup$– LawrenceOct 31, 2019 at 10:30
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Who tells the truth is:
C
because
otherwise there would be contradictions in AC, BC and BD pairs in terms of truth telling
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1$\begingroup$ I edited to hide your reasoning - nice answer - no change to the wording or anything, just the formatting. $\endgroup$– tomOct 12, 2019 at 20:43
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I think the answer is
C.
because
If C is lying, then B must be telling the truth. However, if B is telling the truth then A must also be telling the truth. This is a contradiction, so C must be telling the truth.
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2$\begingroup$ Welcome to Puzzling SE. Note that I put some formatting into your answer so that the answer would not be obvious. You did a nice job of hiding your explanation though. I had to put some words in to make the formatting work. $\endgroup$– tomOct 12, 2019 at 20:46
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As an alternate line of thinking:
Either C or B must be telling the truth, otherwise C has a contradiction: If B doesn't tell the truth, then C is, but if C doesn't tell the truth, then B is.
Therefore
D must be the killer, as he cannot be telling the truth.
This means
A and B are lying, as C is not the killer. Therefore, C is the truth-teller.
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The person telling the truth is
C
because
if A is telling the truth, then B is telling the truth, and there can't be two people telling the truth, so they are both lying. C said that B is lying, which must be true because we just figured out that A and B are both lying. Therefore C is not the killer and is telling the truth.
Since there can only be one person telling the truth, and we know that
C
is telling the truth,
we know there can be no one else telling the truth, which means we now know that D is lying,
and is therefore the killer.
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If D is lying, then D is the killer, therefore both A and B are lying, and C is telling the truth.
If D is telling the truth, then A, B and C are lying because there is only one truth teller. But if C is lying, B must be telling the truth. But now B is both lying and telling the truth - a contradicton!
Therefore:
D is lying, so C is telling the truth and D is the killer.
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As others have said, the person telling the truth is
C
Here's another approach to figuring this out:
If A is the killer, C and D are telling the truth. If B is the killer, C and D are telling the truth. If C is the killer, A, B, and D are telling the truth. If D is the killer, only C is telling the truth.
From this we conclude (since we know there is only one truth-teller) that:
The killer must be D, since that's the only case that gives us a single truth-teller, which is C.
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$\begingroup$ Actually, rot13(vs Q yvrf, gura gur xvyyre qrsvavgryl zhfg or uvz, fb gur xvyyre vf Q). $\endgroup$ Oct 14, 2019 at 5:22
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2$\begingroup$ If A is the killer, then wouldn't D be telling the truth as well? $\endgroup$– Kapten-NOct 14, 2019 at 12:01
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$\begingroup$ @Kapten-N Thanks, I've corrected my oversight. $\endgroup$– theoristOct 27, 2019 at 19:55
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There is only one person is the killer.
My answer is C is telling the truth and D is the killer
A is a liar - C is the killer (A & B both can't say the truth so we consider they are both liars)
B is a liar - C is the killer ( if they are liars that means C is not a killer. )
C telling truth - B is lying ( it is true B is lying because C is not a killer if he was then A & B both were saying the truth)
D is a liar - D says that it wasn't him ( C is telling truth and only one person is telling the truth that means killer id D because he is not telling the truth. )
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C is telling the truth and D is the killer.
A and B make the same claim, that C is the killer. Both are right (telling the truth) or both are wrong (both are not telling the truth); Both can't be right because only one can be. Thus, both are wrong, i.e. C is not the killer. C's claim is that B is wrong, which agrees with the lies of A and B, that C is not the killer. If C's is the one telling the truth, then D's must be wrong, i.e. D is the killer, and not C.
