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^{3}·607 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
130_{10} 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
2^{2}×5×373 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
82_{16} 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
2·13 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 