mersenneforum.org PR 4 # 23
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 2006-06-23, 13:56 #1 Wacky     Jun 2003 The Texas Hill Country 32×112 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?
 2006-06-23, 14:24 #2 Chris Card     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
 2006-06-23, 14:26 #3 axn     Jun 2003 2×32×269 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.
2006-06-23, 14:37   #4
R.D. Silverman

Nov 2003

164448 Posts

Quote:
 Originally Posted by Chris Card 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
Impossible. If A is lying, then his statement is false.
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.

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.

2006-06-23, 14:40   #5
Chris Card

Aug 2004

2×5×13 Posts

Quote:
 Originally Posted by R.D. Silverman Impossible. If A is lying, then his statement is false. But if his statement is false then D is telling the truth.
Why?
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

2006-06-23, 15:01   #6
R.D. Silverman

Nov 2003

164448 Posts

Quote:
 Originally Posted by Chris Card Why? 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
You are indeed correct if one interprets A's statement in the manner you
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".

2006-06-23, 15:10   #7
Chris Card

Aug 2004

13010 Posts

Quote:
 Originally Posted by R.D. Silverman You are indeed correct if one interprets A's statement in the manner you suggest.
If one doesn't interpret the statements in that way, the only solution is
the question setter is lying :smile:

Chris

2006-09-20, 22:23   #8
Maybeso

Aug 2002
Portland, OR USA

27410 Posts

While I was catching up on these puzzles, I noticed the posts for this one are all about interpretation, with no solutions!
Quote:
 Originally Posted by Chris Card 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.
Quote:
 Originally Posted by R.D. Silverman ...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".
If the puzzle is evaluated in this way then:

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.

 2006-10-18, 19:43 #9 olmari     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
 2006-10-19, 02:59 #10 Maybeso     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