[Guest]

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 truthfulness is unknown and they are called Outliers, who do not abide by the land's traditions.

How truthful an Outlier's statements are is unknown, except that they are not the same as those who are Sororeans, Nororeans, or Midroreans. Thus, an Outlier will never make just one or two statements; he will always make three or more.

To catch an aspidochelon, four strong fishermen must throw a huge net over it – then hang on for dear life. At least that’s the theory. No one has ever seen one, much less caught one. The aspidochelon is a gigantic sea monster rumored to be a gastronomical delicacy.

Four husky fishermen, determined to be the first to catch an aspidochelon, set out to sea. As to their group, two are Nororeans; one is a Midorean; and one is an Outlier. The four fishermen discuss this exciting challenge among themselves, below:

Fisherman A

1. I packed lots of food and juice for the hunt.

2. We have been on sea long enough to see our quarry.

3. D is small and weak; he should not be on this hunt.

Fisherman B

1. A is the lead fisherman for this trip because he has seen an aspidochelon.

2. C’s second statement is false.

3. A’s first statement is true.

Fisherman C

1. A packed plenty of grape juice, but not much food for our hunt.

2. I am the lead fisherman, because I have seen an aspidochelon.

3. We have not been at sea long enough to see our quarry.

Fisherman D

1. None of us has ever seen an aspidochelon.

2. All of B’s statements are true.

3. C’s third statement is false.

Which speaker is the Midorean, which is the Outlier, and which two are Nororeans?

Edited January 15, 2010 by K Sengupta

[Guest]

I think something's wrong with the question or at least with my interpretation. Since none of them has seen an aspidochelon there are really only three questions that matter:

Have they been at sea long enough to see their quarry?

Did A pack plenty of food?

Is D small and weak?

So there are eight scenarios: TTT, FTT, TFT, TTF, TFF...etc. I got many different combinations (e.g. if all statements are true, A is an S, B=O, C=N, D=M), but none of the eight scenarios revealed two N's an O and an M.

Am I missing something?

[Guest]

My guess:

A=Nororean

B=Outlier (1 is true, 2 is true, 3 is false)

C=Midorean (1 is true, 2 is false, 3 is false)

D=Nororean

The only way I could work it out was to assume that someone actually has seen the aspidochelon before at some point, possibly on that same trip.

If you take it literally from the intro to the question that no one has seen the aspidochelon, then there is is no way to work it out. D would definitely have a true answer (#1). A or C must have one true answer, since they offer contradicting statements (juice/food and quarry). Since D's #1 answer is true, C's #2 must be false, thus B's #2 is true. That gives us three fisherman with at least one true answer. Since there two Nororeans, this would be impossible. Therefore we must assume that someone has seen the big fish

[Guest]

Here is what I came up with:

C is the Midrorian, A and B are Nororeans, and D is the Outlier.

[Guest]

(O.P. = Original Post)

1 I'll try starting with the assumption that the O.P. statements, other than the discussion, contains all true statements.

2 The O.P. states that "No one has ever seen one", and since the O.P. includes knowledge of the discussion, I will assume that this statement holds true, at least through the end of the discussion -- that is, no aspidochelon ever appeared before the discussion was completed.

3 A3 statement, "D is small and weak" is false, since the O.P. says all four were husky.

4 C2 statement "I am the lead fisherman, because I have seen an aspidochelon" is false, since it contradicts the O.P.

5 B2 statement "C's second statement is false" is true

6 D1 is true, by the O.P.

7 A and C must be the two Nororeans, since B and D have uttered at least one true statement each, so all A and C statements are false.

Now I run into a problem with A2 and C3, since they seem to create a contradiction.

8a A2 statement "We have been on sea long enough to see our quarry" is false, so it must be true that:

8b We have not been on sea long enough to see our quarry.

9a C3 statement "We have not been at sea long enough to see our quarry" is false, so it must be true that:

9b We have been at sea long enough to see our quarry.

Since "No one has ever seen one" it would be impossible for anyone to know how how much time is necessary for one to see an aspidochelon. (Perhaps an aspidochelon doesn't exist, or if it does, perhaps this sea monster surfaces once every thousand years.)

So, 9b appears to be both true and false at the same time.

Some possible explanations:

10 Perhaps there is a subtle difference between "on sea" in A's statement and "at sea" in C's statement that resolves this contradiction.

11 Perhaps the statements in the O.P. are true only until the four fisherman depart, and the Aspidochelon appears sometime during their journey or even during the discussion, altering the truth values of the statements.

12 Maybe another meaning of "husky" is being used in the O.P.

13 It could be that K Sengupta is from Hyperborea (but not from Sororea) and the O.P. contains one or more false statements.

When do we get so see "the real answer?"

[preflop]

K Sengupta

I think you have an error in this puzzle

B & D both make true statements

D(1) None of us has ever seen an aspidochelon (true because in the dialog it states no-one has ever seen one).

B((2) C(2) is false (true because C(2) states he has seen one and so therefore it must be false)

That means that A & C must be Nororeans (all false statements) but if that is the case we get

A(1) false

A(2) false

A(3) false

B(1) false (he claims that A has seen an aspidochelon and we know this cannot be)

B(2) true (established earlier)

B(3) false (false because all of A's are false because he is a Nororean)

C(1) false

C(2) false

C(3) false

D(1) true (established earlier)

D(2) false (none are Sororeans so this must be false)

D(3) true (because all of C's are false because he is a Nororean)

this would have to make both B & D Midroreans (B-FTF, D-TFT) as they both alternate.

You could rearrange D's statements to make it work.