PR 4 # 23

Wacky · 2006-06-23, 13:56

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?

Chris Card · 2006-06-23, 14:24

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

axn · 2006-06-23, 14:26

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.

R.D. Silverman · 2006-06-23, 14:37

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.

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.

Chris Card · 2006-06-23, 14:40

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

R.D. Silverman · 2006-06-23, 15:01

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".

Chris Card · 2006-06-23, 15:10

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

Maybeso · 2006-09-20, 22:23

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.

olmari · 2006-10-18, 19:43

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

Maybeso · 2006-10-19, 02:59

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

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?

2006-10-18, 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

2006-06-23, 14:24	#2
Chris Card Aug 2004 82₁₆ 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 2³×607 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.

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