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-   -   PR 4 # 23 (https://www.mersenneforum.org/showthread.php?t=6045)

 Wacky 2006-06-23 13:56

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?

 Chris Card 2006-06-23 14:24

[spoiler]
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
[/spoiler]

 axn 2006-06-23 14:26

[spoiler]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.[/spoiler]

 R.D. Silverman 2006-06-23 14:37

[QUOTE=Chris Card][spoiler]
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
[/spoiler][/QUOTE]
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.

 Chris Card 2006-06-23 14:40

[QUOTE=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. [/QUOTE]
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=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[/QUOTE]

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=R.D. Silverman]You are indeed correct if one interprets A's statement in the manner you
suggest.[/QUOTE]
If one doesn't interpret the statements in that way, the only solution is
[spoiler]the question setter is lying :smile:[/spoiler]

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=Chris Card;82762]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][QUOTE=R.D. Silverman;82764]...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".[/QUOTE]If the puzzle is evaluated in this way then:

[B][COLOR="Red"]A [/COLOR][/B]is telling the truth means that [B][COLOR="Blue"]C[/COLOR][/B] and [B][COLOR="DarkOrange"]D[/COLOR][/B] are lying, which means that
[COLOR="Blue"][B][COLOR="Green"]B[/COLOR][/B] or [B][COLOR="Magenta"]D[/COLOR][/B] is telling the truth[/COLOR] AND [COLOR="DarkOrange"][B][spoiler][COLOR="Yellow"]C[/COLOR][/spoiler][/B] or [B][spoiler][COLOR="Lime"]E[/COLOR][/spoiler][/B] is telling the truth[/COLOR], which means that
[COLOR="Green"]A and E are lying[/COLOR] OR [COLOR="Magenta"]C and E are lying[/COLOR] AND [spoiler][COLOR="Yellow"]B and D are lying[/COLOR][/spoiler] OR [spoiler][COLOR="Lime"]A and B are lying[/COLOR][/spoiler].

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:
[spoiler]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.[/spoiler]

 olmari 2006-10-18 19:43

Like this?

Could it be?

[spoiler]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[/spoiler]

 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. :goodposting:
:maybeso: Maybeso

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