calamarain
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A quick logic puzzle. A man who happened to be a logician (able to deduce the consequences of things) was walking along a road in a heavenly world. Now the thing about this heavenly world is that there are three types of people there - angels, demons and mortals. Angels will always tell the truth, demons will always lie, and mortals can lie or tell the truth.

He saw two men lying by the side of the road and was curious about them. Neither of them was mortal, that much is known for certain before we begin.

He asked the first man

"Are both of you angels?"

And the man answered him with either a Yes or a No. The logician thought about this, but wasn't about to deduce who was what. He then asked the first man

"Are you both of the same type?"

The man then answered him Yes or No, and the logician was then able to deduce what types the two men were.

So what are the two men? Please include your logic with your answer This isn't my puzzle, sadly.

____________________________
My Holds

CuriousShyRabbit
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I would be able to solve this puzzle if the first question were a little bit different.

Question 1 (to first man): Is your companion an angel?

Question 2 (to first man): Are you both of the same type?

In that slightly different case, here is my solution:

calamarain
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The question can be answered as originally stated. You just have to think about what you know and just as importantly - what the logician knows.

____________________________
My Holds

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[Last edited by calamarain at 09-20-2007 08:33 AM]

Beef Row
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calamarain wrote:
A quick logic puzzle. A man who happened to be a logician (able to deduce the consequences of things) was walking along a road in a heavenly world. Now the thing about this heavenly world is that there are three types of people there - angels, demons and mortals. Angels will always tell the truth, demons will always lie, and mortals can lie or tell the truth.

He saw two men lying by the side of the road and was curious about them. Neither of them was mortal, that much is known for certain before we begin.

He asked the first man

"Are both of you angels?"

And the man answered him with either a Yes or a No. The logician thought about this, but wasn't about to deduce who was what. He then asked the first man

"Are you both of the same type?"

The man then answered him Yes or No, and the logician was then able to deduce what types the two men were.

So what are the two men? Please include your logic with your answer This isn't my puzzle, sadly.

____________________________
"Now I will repeatedly apply the happy-face rule"

calamarain
Level: Smitemaster

Rank Points: 933
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Beef Row wrote:

calamarain wrote:
A quick logic puzzle. A man who happened to be a logician (able to deduce the consequences of things) was walking along a road in a heavenly world. Now the thing about this heavenly world is that there are three types of people there - angels, demons and mortals. Angels will always tell the truth, demons will always lie, and mortals can lie or tell the truth.

He saw two men lying by the side of the road and was curious about them. Neither of them was mortal, that much is known for certain before we begin.

He asked the first man

"Are both of you angels?"

And the man answered him with either a Yes or a No. The logician thought about this, but wasn't about to deduce who was what. He then asked the first man

"Are you both of the same type?"

The man then answered him Yes or No, and the logician was then able to deduce what types the two men were.

So what are the two men? Please include your logic with your answer This isn't my puzzle, sadly.

Click here to view the secret text

×The first answer had to be yes, because if it was no the solution would be immediate, 1: angel, 2: devil

Click here to view the secret text

×Since this is yes, we have either (angel, angel), (devil,angel), or (devil,devil)

Click here to view the secret text

×if the answer to the second question is yes, this could be (devil, angel) or (angel, angel), therefore the answer was no, and they are both devils.

Quite correct. I like this type of puzzle, as a metapuzzle. You don't have all the information but you know under what circumstances it was solved, and from that you can deduce the information and thus the solution

____________________________
My Holds

kzc
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No need to go to all that trouble. We're told right off the bat there are two men lying by the side of the road, so clearly they're both demons.

Ba-da-bum. But seriously, I like this style puzzle as well. It's unlikely you've not exhausted Raymond Smullyan's books on the subject, but in that unlikely case, I recommend doing yourself a favor.

calamarain
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kzc wrote:
No need to go to all that trouble. We're told right off the bat there are two men lying by the side of the road, so clearly they're both demons.

Ba-da-bum. But seriously, I like this style puzzle as well. It's unlikely you've not exhausted Raymond Smullyan's books on the subject, but in that unlikely case, I recommend doing yourself a favor.

Mmmmhmmm. You're quite right, the puzzle's a Smullyan one, though rephrased to use Angels and Demons instead of Knights and Knaves. Didn't want people to see the answer at once.

You also seem to be a prophet I actually ordered two more Smullyan books from amazon.co.uk today! - "What is the Name of this Book?" and "This book needs no title".

And the 'lying by the side of the road' wasn't intentional actually But hey, subconscious pun. Yay!

____________________________
My Holds

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[Last edited by calamarain at 09-20-2007 03:43 PM]

jbluestein
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Beef Row wrote:

Click here to view the secret text

×The first answer had to be yes, because if it was no the solution would be immediate, 1: angel, 2: devil

Click here to view the secret text

×Since this is yes, we have either (angel, angel), (devil,angel), or (devil,devil)

Click here to view the secret text

×if the answer to the second question is yes, this could be (devil, angel) or (angel, angel), therefore the answer was no, and they are both devils.

Isn't the third bit reversed here?



At least, that's the answer I came up with prior to reading all the auxiliary discussions.

Josh

____________________________
"Rings and knots of joy and grief, all interlaced and locking." --William Buck

calamarain
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jbluestein wrote:

Beef Row wrote:

Click here to view the secret text

×The first answer had to be yes, because if it was no the solution would be immediate, 1: angel, 2: devil

Click here to view the secret text

×Since this is yes, we have either (angel, angel), (devil,angel), or (devil,devil)

Click here to view the secret text

×if the answer to the second question is yes, this could be (devil, angel) or (angel, angel), therefore the answer was no, and they are both devils.

Isn't the third bit reversed here?

Not quite. It's the fact that you *know* the logician solved it. If the guy answered yes to the second question, then the problem would be unsolvable, but we know that it was solved. So he must have answered no, it's the only one that leads to a solution.

Oh, and damn you all for inspiring me I've just ordered another Smullyan book. That'll be three books from Amazon now.

____________________________
My Holds

jbluestein
Level: Smitemaster

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calamarain wrote:

jbluestein wrote:

Beef Row wrote:

Click here to view the secret text

×The first answer had to be yes, because if it was no the solution would be immediate, 1: angel, 2: devil

Click here to view the secret text

×Since this is yes, we have either (angel, angel), (devil,angel), or (devil,devil)

Click here to view the secret text

×if the answer to the second question is yes, this could be (devil, angel) or (angel, angel), therefore the answer was no, and they are both devils.

Isn't the third bit reversed here?

Not quite. It's the fact that you *know* the logician solved it. If the guy answered yes to the second question, then the problem would be unsolvable, but we know that it was solved. So he must have answered no, it's the only one that leads to a solution.

Oh, and damn you all for inspiring me I've just ordered another Smullyan book. That'll be three books from Amazon now.

I guess I'm still missing some important step of understanding, then.



Where's my mistake?

Josh

____________________________
"Rings and knots of joy and grief, all interlaced and locking." --William Buck

Rabscuttle
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The logician asks the first man both questions. If he asks the second man the second question, then you can deduce they are both angels.

jbluestein
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Rabscuttle wrote:
The logician asks the first man both questions. If he asks the second man the second question, then you can deduce they are both angels.

And that would be my mistake, then. I for some reason thought he was asking the second man the second question.

I feel much better now...I'm not dumb, I just can't read.

Josh

____________________________
"Rings and knots of joy and grief, all interlaced and locking." --William Buck

calamarain
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jbluestein wrote:
I guess I'm still missing some important step of understanding, then.

Click here to view the secret text

×
Four patterns of answering: YY, YN, NY, and NN

If you do the same grouping of the two beings: AA, AD, DA, DD and then discern how each answers, I get the following:

YY: AA
YN: DA, DD
NY: AD
NN: (nothing)

Which says to me that an answer of YN yields an unsolvable situation, while a YY yields a solvable situation.

Where's my mistake?

Josh

Your mistake's in the YN section.



EDIT: Bah, beaten to it

____________________________
My Holds

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[Last edited by calamarain at 09-20-2007 04:50 PM]