Partial Trial V

Logic Level 1

A, B, and C are on trial. Exactly one of them is guilty. Each makes one statement:

  • A says, "B is guilty!"
  • B says, "C is lying!"
  • C accuses one of A, B, and C of being guilty but you can't hear the statement.

If you knew who C accused and how many of the statements were true, you would know who is guilty. Who is guilty?

B C A

Maggie Miller by Maggie Miller , 27, USA

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4 solutions

Ivan Koswara
Dec 15, 2015

Exactly one of B and C is lying (because B accuses C of lying). Thus the number of lying people is either 1 or 2. If it's 1, then A's statement is correct and B is guilty. If it's 2, then A's statement is incorrect. Regardless of what C says, we can't be sure who the guilty person is among A and C, because C can still be honest or lying. Thus B is guilty .

Note that we don't need to know what C says, as long as we know the number of lying people.

15 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Good analysis of the different cases.

Actually the problem did not require that any of them were telling the truth. So if all of them were lying you could not be sure who was guilty.

Richard Lawlor - 5 years, 5 months ago

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Agreed dumb question.

Giacomo Liberato - 5 years, 5 months ago

If all of them are lying then B and C cause a contradiction.

Ivan Koswara - 5 years, 5 months ago

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It didn't say how many. It could be any combination B could lie A could lie And c could tell the truth etc...

Giacomo Liberato - 5 years, 5 months ago

Actually if its true that any of them cols be guilty and A lied, then why did B not defend against A's accusation and instead called C a liar? That tells me that B is an honest soul and therefore A is true. I got this question wrong and had to think with the explanation for a few minutes before I came to that conclusion . The answer A is true.

Adam Lewis - 5 years, 5 months ago

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Why does B have to defend against A's accusation? There is nothing logically that requires B to do so.

Ivan Koswara - 5 years, 5 months ago

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Well, if you were on trial and being accused you would be obligated to defend yourself unless you had a lawyer. In this case there is none. Unless B is taking the wrap for A or C.

Adam Lewis - 5 years, 5 months ago
Tawaf Nasution
Dec 15, 2015

Correct me if I'm wrong. In my opinion... (Or with this three statements)

  1. If C says that A is guilty, neither A or B or even C is guilty, since this will give an loop reaction or let's just say forth and back truth telling, i don't know how to call it... (Like C : "A is guilty"; A : "B is guilty"; B : "C is lying")
  2. If C says that B is guilty, it means by the chance that A and C are telling the truth, since B said that C is lying and A said that B is guilty.
  3. If C says that C is guilty, it means C is not guilty, since he's not telling the truth (By the B's statement) and since A is telling that B is guilty, the highest chance of guilty is still on the B

That's all, I'm not a good speaker, Seriously. Please re-correct these words if there's a lot of mistakes that I make on this solution. :/

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You wrote perfectly here, Tawaf! ;)

Elizabeth Franck - 5 years, 5 months ago

I also thought in the same way Tawaf. This solution is easier to understand.

Ipshit Shaha - 5 years, 5 months ago

Ivan's solution is by using the number of lying people. My solution is by knowing the C's possible statements.

In other words there are two solutions here. LOL! Yeah, he's smarter than me on solving that problem =w=

Tawaf Nasution - 5 years, 5 months ago

Minor issue. If c isn't lying and accuses themself of the crime than A and b would be lying and only c would tell the truth. Which could make the answer possibly c

Giacomo Liberato - 5 years, 5 months ago

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"Possibly" in your own possibly C is the working adjective in your statement. It was strictly stated in the problem statement that we WOULD KNOW for sure who is guilty, no "possibly?” there.

Saya Suka - 4 months, 1 week ago
Saya Suka
Jan 19, 2021

A says, "B is guilty!"
B says, "C is lying!"
C accuses one of A, B, and C of being guilty but you can't hear the statement.

B is contradicting C, so there exists a liar between them. Thus, at most there would be 2 truths spoken. Let's list the cases one by one.

2 total truths :
1) TTF --> C : A or C --> B guilty
2) TFT --> C : B --> B guilty

1 total truths :
1) FTF --> C : (A or B) or (B or C) --> C or A guilty
2) FFT --> C : A or C --> A or C guilty

Now it's crystal clear that even if we were told that there's one total truth spoken in the trial and who C accused, we would never know if C was telling the truth or not with his accusation; all we can gather is that B would be innocent in this case.

On the other hand, once we're told of the information about the 2 total true statements, it can only mean one thing: A must be telling one of them, so B must be guilty whether or not he spoke the truth. In fact, who C accused does not matter at all, but it might be useful in deducing who the liar is.

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Actually A accuse to B. So B is guilty

0 Helpful 0 Interesting 0 Brilliant 1 Confused

What? That's just a too much short conclusion :/

Tawaf Nasution - 5 years, 5 months ago

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Well thats all. I agree to @Ivan Koswara's statement

A Former Brilliant Member - 5 years, 5 months ago

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