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Need help with a logic puzzle

Old 10-12-06, 10:56 PM
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Need help with a logic puzzle

I have a book of logic puzzles and I think one of the answers is wrong. I wanted to run it by the intelligent folks of DVDTalk and see what you come up with.

There are four suspects in a crime and each makes one statement, although only one of the four speaks truthfully. The guilty one can be deduced from their statements below.

A) B did it.
B) C did it.
C) I did it.
D) Either A or C is the guilty one.

Who is guilty?
Old 10-12-06, 11:06 PM
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Yeah, seems like it's screwed up.

Spoiler:

It could be either B or A.
Old 10-12-06, 11:24 PM
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Yep. You got what I got.

Spoiler:
According to the book, A is guilty
Old 10-12-06, 11:44 PM
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For what it's worth, I'm also getting the same answer:

Spoiler:
A or B
Old 10-12-06, 11:46 PM
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You made my head hurt.

By the way, is it "C. A did it" instead of "C. I did it" ?
Old 10-12-06, 11:47 PM
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I believe that B is still looking for the real killer.
Old 10-12-06, 11:58 PM
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Originally Posted by GatorDeb
You made my head hurt.

By the way, is it "C. A did it" instead of "C. I did it" ?
No, it's "C. I did it"

BTW, this problem is the easiest one in the book. If I posted the hardest one, I think DVDTalk's collective head would hurt.
Old 10-13-06, 12:13 AM
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Go ahead, post some of the harder ones.

If we can figure out how to put a clarinet together I'm sure we can do some logic puzzles.
Old 10-13-06, 12:29 AM
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Originally Posted by hippie68
I have a book of logic puzzles and I think one of the answers is wrong. I wanted to run it by the intelligent folks of DVDTalk and see what you come up with.

There are four suspects in a crime and each makes one statement, although only one of the four speaks truthfully. The guilty one can be deduced from their statements below.

A) B did it.
B) C did it.
C) I did it.
D) Either A or C is the guilty one.

Who is guilty?
B is the guilty one, A is telling the truth.
Old 10-13-06, 12:33 AM
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Originally Posted by hippie68
BTW, this problem is the easiest one in the book. If I posted the hardest one, I think DVDTalk's collective head would hurt.
Why, is it wrong in some particularly spectacular way?
Old 10-13-06, 12:51 AM
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Originally Posted by Heat
Go ahead, post some of the harder ones.

If we can figure out how to put a clarinet together I'm sure we can do some logic puzzles.
As you wish


There is a place called Hyperborea and it is divided into three regions. Those who live in the southern region are known as Sororeans and always speak truthfully. Those who live in the northern region are known as Nororeans and always speak falsely. Those who live in the middle region are known as Midroreans and make statements that are alternately true and false, but in which order is unknown. Lastly, there are a few Hyperboreans whose truthfullness is unknown and they are called Outliers.

The following statements are made by four inhabitants.

A)

1. My statements are not all truthful.
2. We are overworked
3. We are all lucky to be here.
4. We Hyperboreans are favored by the gods.

B)

1. I agree with A's third statement.
2. Every time I see a visitor, I think maybe it is one of the gods, in disguise.
3. I am doing more than my share of the work.
4. My statements are all truthful.

C)

1. My statements are all truthful.
2. D's second statement is false.
3. The gods do not visit us in disguise.
3. We are all overworked.

D)

1. C's first statement is truthful.
2. B's third statement is truthful.
3. My statements are all truthful.
4. The gods frequently visit us in disguise.


Which one is the Sororean, which one is the Nororean, which one is the Midrorean, and which one is the Outlier?


The answer is:
Spoiler:
A. Outlier B. Sororean C. Nororean D. Midrorean


I'll post an even harder one tomorrow night.
Old 10-13-06, 12:56 AM
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Originally Posted by dork
Why, is it wrong in some particularly spectacular way?
No, the one in my original post was the only wrong one I found, but they are in the book in order of difficulty and it was first in the book. It should have been easy, but the authors goofed.
Old 10-13-06, 01:05 AM
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Regarding the hyperboreans...
Spoiler:
Here is what I got:

A: Midrorean (his first and third statements are true, second and fourth are false)
B: Sororean (all his statement are true)
C: Nororean (all his statements are lies)
D: Outlier (first two statements are true, third and fourth are lies)

Note that I have the same B & C as the book, with A & D switched.

But... if D were the Midroean (like the book says) then his answers would have to alternate between truth and lies. But if B only tells the truth and C only lies, then Dís first two statements are true thus D has to be the Midroean.

Last edited by Heat; 10-13-06 at 01:09 AM.
Old 10-13-06, 01:06 AM
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Maybe you should not post the spoiler right away?
Old 10-13-06, 01:06 AM
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Originally Posted by hippie68
I have a book of logic puzzles and I think one of the answers is wrong. I wanted to run it by the intelligent folks of DVDTalk and see what you come up with.

There are four suspects in a crime and each makes one statement, although only one of the four speaks truthfully. The guilty one can be deduced from their statements below.

A) B did it.
B) C did it.
C) I did it.
D) Either A or C is the guilty one.

Who is guilty?
The answer is clearly A. "B did it".

1. B and C say the exact same thing, but since only one person speaks the truth, they both must be lying.
2. D says either A or C, which is another contradiction.
3. A is the only one saying B, which then must be the truth.
Old 10-13-06, 01:16 AM
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Originally Posted by Heat
Regarding the hyperboreans...
Spoiler:
Here is what I got:

A: Midrorean (his first and third statements are true, second and fourth are false)
B: Sororean (all his statement are true)
C: Nororean (all his statements are lies)
D: Outlier (first two statements are true, third and fourth are lies)

Note that I have the same B & C as the book, with A & D switched.

But... if D were the Midroean (like the book says) then his answers would have to alternate between truth and lies. But if B only tells the truth and C only lies, then Dís first two statements are true thus D has to be the Midroean.

You are mixed up heat. D's first statement is false.
Old 10-13-06, 01:17 AM
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Originally Posted by postermen
The answer is clearly A. "B did it"...
The question isn't "who is telling the truth?", the question is "who did the crime?"

Spoiler:
And yes, A could be telling the truth since when he says "B did it", neither B, C, nor D contradict him.

But D could also be telling the truth since neither A, B, nor C contradict "A" as being the criminal.

That's where "A or B" come from.
Old 10-13-06, 01:18 AM
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Originally Posted by Heat
Regarding the hyperboreans...
Spoiler:
Here is what I got:

A: Midrorean (his first and third statements are true, second and fourth are false)
B: Sororean (all his statement are true)
C: Nororean (all his statements are lies)
D: Outlier (first two statements are true, third and fourth are lies)

Note that I have the same B & C as the book, with A & D switched.

But... if D were the Midroean (like the book says) then his answers would have to alternate between truth and lies. But if B only tells the truth and C only lies, then Dís first two statements are true thus D has to be the Midroean.
Spoiler:
D's first statement is false, since the Nororean (C) only lies. D's second statement is true since the Sororean (B) only tells the truth. D's third statement is false and D's fourth statement is true because the Nororean (C) said the opposite.
Old 10-13-06, 01:25 AM
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You're right. I went back over my worksheet and for some reason
Spoiler:
I had D's first statement as being truthful (when it isn't) and I hadn't noticed that D's fourth statement and C's third statement were related.
Old 10-13-06, 11:48 AM
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Originally Posted by postermen
The answer is clearly A. "B did it".

1. B and C say the exact same thing, but since only one person speaks the truth, they both must be lying.
2. D says either A or C, which is another contradiction.
3. A is the only one saying B, which then must be the truth.
D isn't a contradiction. If D is telling the truth, then A is guilty. None of the lies from A, B, or C would contradict that.
Old 10-13-06, 12:13 PM
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Logically if she weighs as much as a duck she is a........
Old 10-13-06, 12:25 PM
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I thought I was an idiot, but yeah that first puzzle is messed up.
Spoiler:
Could work as A or B
Old 10-13-06, 12:30 PM
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An easier way to think of it might be to plug in values we would all recognize, so the puzzle might look like this:

There are four Otters and each makes one statement, although only one of the four speaks truthfully. The Otter who loves Bandoman can be deduced from their statements below.

Kittydreamer) Vibiana loves Bandoman.
Vibiana) Bandoman loves himself.
Bandoman) I love myself.
Groucho) Either Kittydreamer or Bandoman loves Bandoman.

Who loves Bandoman?


This is of course a trick question.

Spoiler:
Nobody loves Bandoman
Old 10-13-06, 01:23 PM
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I think you have to assume guilt for each one and then work it out.

Spoiler:


B shows that A is telling the truth, but then D proves that A is a liar.

If you assume A is guilty, then A, B & C lied, thus making D the truthful one.

If you assume B is guilty, then B, C & D lied, thus making A the truthful one. B is a liar.

C can not be guilty because three suspects would be telling the truth, but he's a liar.

If you assume D is guilty, then they all would be liars. B and C are liars, so A would have to say D to be telling the truth. So that makes A a liar and D not guilty and telling the truth.



Alright! that didn't make a bit of sense. It still doesn't prove B's innocence. I give up...Still have a headache. I'll try the other one now.

Last edited by MysteryX01; 10-13-06 at 02:58 PM.
Old 10-13-06, 01:44 PM
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Hyperborea breakdown:
Spoiler:
A1 means A can't be all true or all false. A1 is True.
D1 means D can't be all true. D3 is False.
If D1 is True, C is all true, D2 is False, D must be Outlier (TFF), B is all false, A alternates, A1 is True, A2 is False != B3 is False, so D1 can't be True.
If D1 is False, B is all true, D2 is True, D3 is False, D4 is True, D is Midorean (FTFT), C is all false, A is Outlier.


das

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