One of Each (Outliers of Hyperborea Part III)

Among four Hyperboreans one is a Sororean, one is a Nororean, one is a Midrorean and one is an Outlier. They make the following statements:

1. 1. I am the Outlier.
   2. D is not more truthful than I am.
   3. B is the Sororean.
2. 1. A is the Outlier.
   2. C is not the Sororean.
   3. I am not the Midrorean.
3. 1. A is not the Outlier.
   2. B is not the Sororean.
   3. I am more truthful than D is.
4. 1. B is not the Nororean.
   2. A's second statement is false.
   3. C's third statement is false.

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

(Source: Challenging False Logic Puzzles by Norman D. Willis)

A obviously cannot be the Sororean. If that were the case, then he wouldn't have said he is the Outlier.

If A is the Midrorean, then the order is FTF. If, per A2, D is not more truthful than A is, then D is either the Nororean or the Outlier. Additionally, because A3 is false, then B is also either the Nororean or the Outlier, leaving only C to be the Sororean. All of C's three statements check out under this assumption. So far, so good, now on to the other two.

What if B is the Nororean? B1 and B2 check out as false but B3 does not. This means D is the Nororean then, right? Well that can't be the case either, because D1 is true and Nororeans always lie.

So the assumption that A is the Midrorean has to be thrown out now. How about A being the Nororean? A's statements can all feasibly be false. Also, the falsity of A3 means that B is not the Sororean, allowing only C or D to be Sororean.

What if C is the Sororean? All of C's statements check out. This means that either B or D is the Midrorean. B, however, cannot be the Midrorean because the only possible order is FTF and B2 is false under these assumptions. If D is the Midrorean, then the order of statements has to be TFT. However, this doesn't pan out either, because C3 is false.

So the assumption that C is the Sororean is necessarily false. This doesn't immediately defeat the assumption that A is Nororean. This assumption still has one more chance at life if D is the Sororean. Indeed, all of D's statements are feasible. All this leaves is who is the Midrorean and who is the Outlier.

Consider the possibility that B is the Midrorean. The order is constrained to FTF and this works out. Lastly C must be the Outlier. Under all the previous assumptions, C's statements are true, true and false, respectively, behavior befitting an Outlier.

Final answer: A is the Nororean, B is the Midrorean, C is the Outlier and D is the Sororean.