Tuesday, January 3, 2017

An Outlier (Outliers of Hyperborea Part II)


Four Hyperboreans are engaged in conversation. One is a Sororean, one is a Nororean and one is a Midrorean. The fourth speaker is an Outlier.

From their statements below, which one is the Sororean, which one is the Nororean, which one is the Midrorean, and which one is the Outlier?
    1. I am the Outlier.
    2. D is the Nororean.
  1. A's first statement is true.
    1. I am not the Outlier.
    2. B is not the Midrorean.
  2. C's first statement is true.
(Source: Challenging False Logic Puzzles by Norman D. Willis)

For me, the first assumption that seemed especially productive was assuming that A is the Midrorean. If A is the Midrorean then A1 is false and A2 is true. This means that D is the Nororean and, in turn, that C's first statement is false, making C the Outlier. The only remaining possibility for B is being the Sororean, but this cannot be the case because B said that A's first statement is true and it was assumed that A was the Midrorean.

So, now, consider the implications of A being the Nororean. A1 and A2 both check out as false. B's statement is false and so B is constrained to either being the Outlier or the Midrorean. Consider what happens if B is the Outlier. Both of C's statements check out, which makes C the Sororean. Lastly, D can feasibly be the Midorean.

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

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