There are only four cases. Try each case and see which one does not yield a contradiction.
I have a logical riddle that I need help solving :
There has been a murder and four suspects are being interrogated.
*A says that B did it.
*B denies responsibility, and says it was D.
*C adds that it wasn't him.
*D declares that B lied.
We know that only one person told the truth. But who was it ?
Assume that A told the truth. So, B did it and lied. So, C and D told the truth. So, we find that 3 people told the truth - a contradiction. So, A lied.
Assume that B told the truth. So, D did it and lied. So, C told the truth. So, 2 people told the truth and we get a contradiction. So, B lied.
Assume that C told the truth. So, D lied. But this implies that B told the truth and we get a contradiction as 2 people told the truth. So, C lied.
So, D told the truth and C did it.
Wait, I have a similar riddle to this one :
We know that thiefs always lie and that knights always tell the truth.
A, B and C are either knights or thiefs.
*We ask A if he's one or the other but we can't hear what he says.
*B says that A said he was a Thief.
*C says that B told a lie because he's a thief.
Question : What is the identity of B and C ?
That's interesting ... I have a similar question.
Let's say we meet ''D and E''. D says that at least one of the two is a thief.
What can we say about the identity of D and E ?
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If D was a knight, then E would be the thief. If D was the thief, then he wouldn't say he was himself the thief. And if D was the thief, he could falsely accuse E of being the thief.
OK, I just have one more little thing I need help with :
Suppose you have a piece of paper in front of you.
*The front side of the paper says : ''The sentence on the back side of the paper is false''.
*The back side of the paper says : ''The sentence on the front side of the paper is false''.
Are we able to conclude anything about whether the front side or back side is true or false ?
Assume that the sentence on the front side of the paper is true. Then, the sentence on the back side of the paper is false. This implies that the sentence on the front side of the paper is true, which is what we initially assumed.
Assume that the sentence on the front side of the paper is false. Then, the sentence on the back side of the paper is true. This implies that the sentence on the front side of the paper is false, which is what we initially assumed.
So, one of the statements is true and the other is false.
Would both sides have the same value if the back side said the front side was true ?
*The front side of the paper says : ''The sentence on the back side of the paper is false''.
*The back side of the paper says : ''Thes sentence on the front side of the paper is true''.
Assume that the sentence on the front side of the paper is true. Then, the sentence on the back side of the paper is false. This implies that the sentence on the front side of the paper is false, which gives us a contradiction.
Assume that the sentence on the front side of the paper is false. Then, the sentence on the back side of the paper is true. This implies that the sentence on the front side of the paper is true, which gives us a contradiction.
So, the statements are logically inconsistent and we cannot say that either is true/false.