Friday, January 6, 2017

Four for the Races (Outliers of Hyperborea Part VII)

Four Hyperboreans are practicing for the upcoming chariot races. They are known to be a Sororean, a Nororean, a Midrorean, and an Outlier. They make the following statements:
    1. This race track is slow.
    2. D is doing so well in practice that he will win.
    3. C is the Outlier.
    1. A's first statement is true.
    2. I am the Midrorean.
    3. D is the Nororean.
    1. This race track is fast.
    2. I agree with B's second statement.
    3. I am not the Nororean.
    1. I am doing so poorly in practice that I will lose.
    2. B's second statement is false.
    3. A is the Sororean.
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)

Consider the notion that B is the Midrorean. If so, then B2 is true and his other statements are false. This means that A1 is false and that D is not the Nororean. It follows from the first of these implications that A is either the Nororean or the Outlier because of the falsity of at least one of his statements and that the race track is in fact fast.

What if A is Nororean? Then A2 and A3 are also false. This means that D is not doing well in practice, not well enough to win anyhow and also that C is not the Outlier. Because, in addition to this, B is believed to be the Midrorean and A the Nororean, only D can be the Outlier. Also, C must be the Sororean under these assumptions.

Do the assumptions work? It can be seen easily that all of C's statements can be true. Additionally, D can be the Outlier if his statements true, false and false.

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

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