20060623, 13:56  #1 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
PR 4 # 23
Five suspects were rounded up in connection with the famous "Cock Robin Murder." There statements were as follows:
A: "C and D are lying." B: "A and E are lying." C: "B and D are lying." D: "C and E are lying." E: "A and B are lying." Who is lying? 
20060623, 14:24  #2 
Aug 2004
2×5×13 Posts 
maybe I've gone wrong, but I can see two answers: A, B and D lying, C and E truthful A, C and E lying, B and D truthful 
20060623, 14:26  #3 
Jun 2003
2×5^{2}×97 Posts 
Insufficient data. We don't know which statements they are refering to while making the claim "lying". It can't be the statements given in the problem  that would lead to a chicken and egg situation.

20060623, 14:37  #4  
Nov 2003
2^{2}×5×373 Posts 
Quote:
But if his statement is false then D is telling the truth. But your case 1 says D is lying. In case 2 If A is lying, then C must be telling the truth. I can't find any combination that doesn't lead to a contradiction. Suppose A is telling the truth. Therefore C & D are lying. But if C is lying, then D is telling the truth > contradiction Suppose A is lying. Then C & D are telling the truth. But if C is telling the truth then D is lying, contradicting A. A can be neither lying nor telling the truth. Something doesn't add up. 

20060623, 14:40  #5  
Aug 2004
82_{16} Posts 
Quote:
If A is lying then it's not true that C and D are lying, which means C or D or both are telling the truth. Chris 

20060623, 15:01  #6  
Nov 2003
1110100100100_{2} Posts 
Quote:
suggest. i.e. the negation of "C and D are lying" is C *or* D is telling the truth and not "C *and* D are telling the truth". 

20060623, 15:10  #7  
Aug 2004
2×5×13 Posts 
Quote:
the question setter is lying :smile: Chris 

20060920, 22:23  #8  
Aug 2002
Portland, OR USA
2×137 Posts 
While I was catching up on these puzzles, I noticed the posts for this one are all about interpretation, with no solutions!
Quote:
Quote:
A is telling the truth means that C and D are lying, which means that B or D is telling the truth AND [COLOR="Yellow"]C or [COLOR="Lime"]E[/COLOR] is telling the truth[/COLOR], which means that A and E are lying OR C and E are lying AND [COLOR="Yellow"]B and D are lying[/COLOR] OR [COLOR="Lime"]A and B are lying[/COLOR]. A is telling the truth implies that either A is lying or D is both telling the truth and lying. So A is lying. Evaluating the other suspects statements in a similar way gives two possible solutions: If B and D are telling the truth, then A, C, and E are lying. If C and E are telling the truth, then A, B, and D are lying. 

20061018, 19:43  #9 
Jul 2005
Vaasa, Finland
26_{10} Posts 
Like this?
Could it be?
A: "[B]C[/B] and D are lying." D: "[B]C[/B] and E are lying." B: "[B]A[/B] and E are lying." E: "[B]A[/B] and B are lying." only remaining one is : C: "B and D are lying." In other words: A says "C and [B]D[/B] are lying"... now [B]D[/B] [I]CONTRADICTS[/I] HIM and says "C and E" are lying .. coz of that, u can't trust both of them same way .. B: "[B]A[/B] and E are lying." E: "[B]A[/B] and B are lying." only guy to trust is C: "B and D are lying." .. nobody contradicts the poor fellow 
20061019, 02:59  #10 
Aug 2002
Portland, OR USA
2×137 Posts 
I just figured out that my solution agrees with Chris Cards (Doh!) My earlier impression was that Chris had changed his interpretation during his exchange with Bob.
So I second Chris' answer. Maybeso 