One Is an Outlier (Outliers of Hyperborea Part V)

Outliers, although few in number, occasionally make their presence known. Hyperboreans are either Sororeans, Nororeans, Midroreans, or those few Outliers. As to the four inhabitants who make statements below, little is known as to their standards of veracity, except that exactly one of them is an Outlier.

1. 1. B is the Outlier.
   2. D is a Sororean.
   3. C is a Midrorean.
2. 1. I am not the Outlier.
   2. A is a Nororean.
   3. C is not a Midrorean.
3. 1. I am not a Midrorean.
   2. B is not the Outlier.
   3. D is a Sororean.
4. 1. I am a Sororean.
   2. B is the Outlier.
   3. A is a Midrorean.

To which group does each of the four Hyperboreans belong?

First, entertain the proposition that A is a Sororean. If A is a Sororean, then D is also a Sororean, but D tells us that A is a Midrorean, which is a contradiction. So A is not a Sororean.

What if B is a Sororean? Then A is a Nororean and the possibilities for Outlier are now restricted to either C or D. If C is the Outlier than his statements are, respectively, true, true and, by implication, false. (Three true statements in a row would make for a Sororean.) Lastly, all of D's statements can be assigned a value of false without contradicting anything else, making him a Nororean.

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